Hyperlinguist is a great and undervalued trait, but there are some real issues with how it is actually implemented in the game's systems and as a result it can easily become unbalanced (in the character's favor or against them).
One of the things that I'd argue is that there are actually two game mechanics going on here, both of which are being pushed together.
Unfortunately, we don't really have a lot of light into the "learning a language in a day" thing. Someone who puts 30-some hours into language learning nowadays can learn basic survival tools ("Hello! Can I have some water? Where is the bathroom? Thank you.") in a language, but would hardly be considered fluent. At the same time, people with immersion and good linguistic talents claim to be able to learn to speak languages in matters of weeks and months, though this is likely more hardcore than an average Joe would do.
As someone who is both a long term fan of Eclipse Phase and a shorter-term teacher of English to speakers of foreign languages, I can tell you that there is a massive gap between "functional" and desirable levels of performance as well.
Basic Skill Learning Rules
Eclipse Phase is notorious for being a game that doesn't really have character advancement, and advancement by default is a slow and laborious process only suited for games with simulspace training sessions, long downtimes, and generous Rez Point rewards.
Characters may also spend Rez Points to increase existing skills or
learn new ones... As a rough timeframe, this should require around 1
week of learning per skill point. (EP, 152)
Now, let's look at the variables that can be changed here. 1/3 of the time and experience is clearly an indication that we can gain three skill points per Rez Point (or 3 for 2 once we get past the 1-60 optimal zone). There's some ambiguity whether that 1-60 level includes attribute bonuses, but for the sake of our discussion we'll pretend that we can spend 20 Rez in a go to increase our language level to 60.
If we reduce the time commensurately, this would require 20 weeks of instruction, which is more like what you'd see for a "desirable" turnaround for learning in real life, the sort of thing where dedicated individual instruction and a highly motivated learner is involved. 60 weeks of training and practice would be the default learning time, which is perhaps a more realistic number.
Now, I don't know what you're seeing, but for me this seems to contradict a certain part of the trait's descriptions, namely the one day rule, but it's a thing that would be a little underwhelming for players, especially given the fact that Eclipse Phase allows very few situations where one could be translating without digital assistance (though languages could make a key plot point in certain situations where a basilisk-based digital virus threat exists, appropriate safety measures would allow any basilisk-based virus to be quarantined into low-resolution oblivion). Any sufficiently obscure language to be impossible to use digital translation for would likewise have issues with accessibility for the purposes of taking advantage of Hyperlinguist's learning (the standard rules for using a skill to train it still exists under Hyperlinguist logically).
As such, as a GM I would lean more toward the side of giving too much power to the Hyperlinguist feat.
The Potential Interpretations (conservative to fair to cheesy)
1/3 Price, 2-to-3-day Points
Now, in the grand scheme of things, this is actually quite a good deal. You shave 66% off of the learning time, and get through a language in an incredibly short amount of time. Realistically, this is the amount of time the average person would need to access enough of a language to have an effective corpus for making decisions from and build a solid schema so that they can begin incorporating figurative language and so forth. In play terms, it's somewhat unsatisfying for players. It also means trickling out Rez, which is how the game is meant to be played (or so I believe; it's been a while since I last saw talk about how the designers viewed Rez Points) since sessions are supposed to reward relatively little on their own.
I would incorporate this rule at my table for characters simply immersing themselves in a language, not seeking out training. The only gripe I have with it is that Hyperlinguist is so expensive compared to taking languages in character creation that you're really having them pay a lot for not a huge amount of benefit. You might also not let them make any strategic use of their new language skills; the gang of neo-primitives they wanted to infiltrate has already done what they set out to do by the time they learn the language.
1/3 Price, 1-day Point
I like this one the most; it's powerfully quick (learn a language in 60 days) to the point where it actually stands out as a transhuman ability; some very few baseline humans might be able to achieve this feat, it doesn't force characters to take steps (like some faster methods do), and it's really powerful nonetheless.
Characters burning financial assets or relying on favors for training (or using digital resources, if the language is readily available in that manner) would use this rule at my table.
1/3 Price, 1-day "Advancement"
Same as above, only using 5/10 point increments. This allows for really advanced improvement. You would still want players to pay for the language normally, which would mean that they would be able to spend multiple Rez points at a time (of course, you could reduce that if there are insufficient points or characters want only a little learning).
I think this is too fast, as it would leave a character with fewer than two months to develop a whole language schema. Asyncs may be able to learn at this rate, relying on creepy paranormal elements, but it'd be largely implausible except with the aid of simulspace.
1/3 Price, 1-day Fluency
I thought the above option was too fast, but you could theoretically allow a character to spend 1/3 the normal Rez price to learn any amount of the language skill in a single day. I think that this hinges too heavily on an ambiguity, and stretches the boundaries of reality.
1/3 Price, "Instant" Gain
See above. You would still likely limit the ability to improve languages to an off-screen moment. The advantage of doing this is that it does actually make the Hyperlinguist feat super-useful, albeit super-powerful in its context. It changes the balance of the game in a way that nothing else does.
Free Language, Just Add 24 Hours
This is a tempting interpretation, but ignores half of the rules as written. CP poured into the Hyperlinguist ability can be used in place of a theoretically infinite amount of Rez Points, so you would have to be careful about allowing this interpretation in a game where Hyperlinguist would appear frequently.