In short, this feature will work on magically created weather
Features in 5e do what they say they do. If the feature was meant to exclude a particular category of weather (like weather created by a magical source) then the spell would describe those exceptions. Since the feature doesn't make any exceptions, if a magical effect creates weather, then this ability can affect it.
With that being said, there is one caveat...
It depends on the DM's definition of "weather"
In 5e, terms that do not have explicit game definitions are meant to be interpreted based on their natural language definitions.
Although a section on weather does exist in the DMG, it doesn't define weather as anything explicit in game terms. So we use the natural definition, which merriam-webster defines as:
the state of the atmosphere with respect to heat or cold, wetness or dryness, calm or storm, clearness or cloudiness
At first glance, everything looks fine. But colloquially, not every single atmospheric effect is what I would call "weather." And that's where your sticking point is.
Do these spells actually count as weather?
It seems a silly question, but think about it. If you use a leaf blower to clear your lawn, does that count as weather? If I stir the water in my glass to make a miniature whirlpool, is that weather? If not, what makes those that different from using magic to create these exact same effects only on a larger scale?
In fact, there is even some precedent that not every atmospheric effect is weather. When asked about the use of create or destroy water on a vampire's mist form, Jeremy Crawford, lead rules designer, replied:
Create or destroy water—the spell can destroy a 30-foot cube of fog. A vampire's mist form is not fog or any other weather effect.
A DM is well within their right to rule that one or more spells that have an effect on the atmospheric conditions around a character do not constitute weather. Taking a previous example, it would be akin to them saying "gust of wind doesn't create weather, it's just a magic fan blast. That's not weather." If they make such a ruling, you're out of luck. The feature only works on weather, and your DM said that particular effect isn't weather. However, the DM is just as justified saying "oh, yeah. That's totally weather." and then you're good to go.
Since there's no solid answer on this specific scenario from any official rule clarification (as far as I could find) the answer then boils down to: You might be able to as long as your DM rules that the magical effect really does constitute "weather" instead of magical manipulation of the atmosphere (like a fan on a hot day, only magical instead of mechanical).