Unless it's a delayed reaction or an ass-pull by the author, my bets are on it being not a straight up gender change but instead a "your inner desire, even if you don't fully get it" kind of thing.
Explains why the president basically just got a penis but is still pretty much feminine-looking to everyone else, why Hinata (who was already bordering the line between male and female look-wise) changed genders but not in an extravagant way, that one girl in the library basically looks like a girl except for the penis, etc.
Could be wrong, but it does make sense of why every transformation isn't a straight-up original gender -> opposite gender.