It depends on exactly what we’re talking about
Up front, be aware that while Curse of Strahd only notes that Barovia is found in a remote demiplane far from the rest of the multiverse and doesn’t give more detail on that plane, there is more detail to be found. Curse of Strahd is designed to be viable as a stand-alone product, so you don’t need that additional information to run it, but if you’re interested, it does exist.
However, it also greatly complicates this question because the adventure effectively exists in two not-entirely-compatible states: standalone adventure, or part of a wider dedicated campaign setting. In the standalone adventure, the mists are the mists and Strahd controls them. In the greater campaign setting, Strahd has his poison mists, which are mostly the same as those in the standalone adventure but maybe slightly differet, and then there are also other mists, “Mists” I’ll call them, that Strahd definitely does not control. The interaction of the Vistani with each of these three mists also varies—probably.
As might be clear, it’s really hard to talk about the mists and Vistani with any certainty. The adventure and the campaign setting are both designed to make these things mysterious and intentionally undefined—to allow a DM to fill in the blanks as they like.
Publication History of the Ravenloft Adventure
Some background: Strahd and Barovia debuted in an adventure first published for AD&D in 1983, Ravenloft. That adventure is easily among the most classic and popular D&D modules of all time, and has been republished as House of Strahd for 2e, Expedition to Castle Ravenloft for 3e (specifically, the “v.3.5 revised edition”), and now Curse of Strahd for 5e (there was no proper 4e iteration, but Castle Ravenloft was a board game based on simplified 4e rules that also covered the adventure).
In every case, the adventure can be run by itself, without caring about where Barovia is or what exists outside of its borders. The DM is free to ignore it, or make up their own greater world. Expedition to Castle Ravenloft even includes explicit details of how to include Barovia as a remote region of Karrnath (Eberron), Faerûn (Forgotten Realms), or even Europe (d20 Modern), in case a DM wants to add the adventure to an existing campaign in one of those settings.
Demiplane of Dread Campaign Setting
There is also a Ravenloft campaign setting, also known as the Demiplane of Dread. This is the demiplane that Curse of Strahd refers to. It contains a number of Domains, like Barovia, each with their own Darklord, like Strahd. It is full of mist and mystery and death and fear. It’s primarily described in 2e’s Ravenloft: Realm of Terror and 5e’s Van Richten’s Guide to Ravenloft. The former is the foundation for a whole lot of 2e content; the latter is the latest iteration of that content. I regard both—along with various other 2e sources I implicitly refer to—as canonical but unreliable.
Mists: Strahd’s poison mists vs. the true Mists
Crucially, the wider Ravenloft setting is built around Barovia, and a lot of the themes of Barovia are generalized for the entire demiplane. That includes the mists. Originally, in the adventure, Strahd controlled poisonous mists that prevent anyone from leaving—as much to keep players within the designated sandbox as anything else.
Within the wider setting of Ravenloft, the Mists have a much more expanded role. They are insidious, omnipresent, and full of power. They cover the demiplane and can even extend out into the wider multiverse, and those who get lost in the mists other planes can find themselves in the Demiplane of Dread when the mist clears.
But Strahd still kept his own poison mists. They don’t have the power of the true Mists, but as Darklord, closing the borders of Barovia is within his power, and the poison mists are how he does it. It isn’t automatic that every Darklord can do that, and it doesn’t necessarily involve mist for others; that’s just part of Strahd’s personal Domain.
Crucially, Strahd doesn’t control the true Mists. Strahd controls Barovia, to an extent, and nothing more. Within the greater Demiplane of Dread, Strahd is, first-and-foremost, a prisoner—and Barovia is the prison, and the Mists are metaphorically, the bars.
The only time a Darklord was ever able to engineer the escape of anyone from Ravenloft was when Azalin (Darklord of the domain of Darkon) caused the Grand Conjunction. This basically made the whole of Ravenloft overlap with the Material Plane, allowing for relatively easy egress. A lot of people did escape—nearly including Azalin and Strahd, except that they both ruined their own chances because Ravenloft is, above all, a psychological trap. The Grand Conjunction was a once-ever event, and took an enormous amount of effort on Azalin’s part to bring to pass. Strahd does not have that kind of capacity.
The Dark Powers
The Mists are generally assumed to be under the control of the “Dark Powers”—note that these are very, very distinct from Strahd, who is a Darklord. Darklords are prisoners who are psychologically—at a minimum—tortured by Ravenloft. Though they are “lord” of their Domain, their power over it is sharply limited so as to just feed into their own personal vicious cycle. The Dark Powers are—we presume—the ones behind the Mists, the Domains, the Darklords. They are the ones, we assume, who benefit from the very particular ways in which Darklords are tortured. Their control over Ravenloft appears to be near-total, and the Mists are their primary tool for controlling it—we assume. But we can’t quite rule out the possibility that the Mists exist independently from the Dark Powers, and may not actually be in their control at all.
But we think they are because the Mist has been known to trap a group into the Demiplane of Dread, and then the Dark Powers set a task before them, with the promise of freedom on its successful completion—a promise that is generally fulfilled. While a rare event from Ravenloft’s perspective, this is effectively the “default” scenario for player characters to adventure there. There are several other instances of the Demiplane of Dread letting people go—after all, while Ravenloft holds onto everyone as a matter of course, it’s the Darklords that the Dark Powers actually care about.¹ Conjunctions are known to be rare-ish occurrences where Ravenloft and another plane “overlap,” so that one can walk out of one and into the other. Again, we assume that the Dark Powers control when and where they happen, but maybe they’re just random.
But it’s impossible to know any of that with much certainty. Van Richten should certainly be regarded as an unreliable source of information—Van Richten’s Guide is probably weakest with respect to the Dark Powers, at times wildly contradicting previous sources. Those sources, of course, should also be viewed with some skepticism, though it’s abundantly clear that the term Van Richten uses, “vestige,” at least as previously used in Dungeons & Dragons, describes nothing remotely like the Dark Powers. Ultimately, very, very little is known about the Dark Powers, and almost everything we think we know about them, is largely guesswork from circumstantial evidence left by the few overt actions they take.
The Vistani and the mists, one way or the other
Anyway, to the heart of the question, the first question is which mists we’re talking about: the true Mists of Ravenloft, or Strahd’s poison mist. Within the context of the stand-alone adventure, it’s the poison mists, and Strahd can, in fact, allow someone through those—Vistani or otherwise. On the other hand, within the Demiplane of Dread, the Vistani are known to make, and even sell, elixirs that grant immunity to those poison mists—it’s possible the Vistani in question didn’t actually need Strahd’s assistance for that.
What if, in the adaptation of the adventure to the wider Demiplane of Dread, we see this scene as involving the true Mists? On that point, it’s important to remember that the Vistani are deeply enigmatic. Extremely little is known about what they actually can do in Ravenloft, or how they fit into matters—they are as much an uncertainty as the Dark Powers are. However, it has long been theorized that the Vistani—unlike very literally anyone else, only possibly excepting actual deities—can, in fact, defy the Dark Powers and/or the Mists. If this is the case, it’s possible that the Vistani here didn’t just pass through Strahd’s mists, but also through the true Mists—something otherwise impossible, and certainly not something Strahd is capable of enabling. But that’s only one theory.
Another possibility is that the Dark Powers could simply allow one Vistani or another to leave through the Mists, possibly even at a time coinciding with Strahd asserting that he was doing so. It may have simply amused them to make it look like he was able to do that. We know that they can do it, anyway.
There is also a case of a Darklord being let go, but that was... a deeply stupid situation that has more to do with arguments among IP owners than it does to do with how the demiplane was actually intended to work. As far as I know, it’s been long-since been ret-conned so that Lord Soth was either never brought to Ravenloft, or else was simply returned immediately to Krynn when he was. His tenure as a Darklord is not canon.
On the other hand, Vecna’s escape from Ravenloft, as detailed in Die, Vecna, Die!, is definitely canon. Uniquely, however, Vecna wasn’t released—he escaped. Which should have been impossible, but Vecna didn’t ascend to be God of Cheating for nothing.