When someone sneezes - yes, exactly this. Specifying would sound very weird here (also as you've seen there are different approaches to this), because when you drink, you drink to someone's health, even someone absent, and here to whose health you could... say this, if not the person who sneezed? ;)
Anyway, something that was not clear enough from my comment from last month: if you were to precise 'whose health' while drinking, delete the 'na' part, say simply "Twoje zdrowie!"
There was nothing to fix, Jellei. WquDT is wrong, "precise" can be used as a verb.
The full Oxford English Dictionary defines the verb TO PRECISE as to make PRECISE or definite; to define precisely or exactly; to particularize.
Congratulations Jellei, your command of English is awesome!
Next time, don't give in so easily!! :)
In Russian, we often drink a toast za zdorowja, "to health," not na zdorowje. We say na zdorowje, for example, if I put a bowl of soup on the table for my friend, and he thanks me spasibo, I answer na zdorowje (for his health) instead of the common pożalujsta for "you're welcome."
If my friend thanks me for passing him a hammer, I would say pożalujsta.
Sneezing would be bud' zdorow/zdorowa as Evgen First wrote in the previous comment.