I have seen mold on ceilings in bathrooms with exhaust fans.
1) Caulk around the exhaust fan, so when it runs the fan does not pull
in humid attic air when it is running. Exhaust fans will pull air from
wherever they can get it. If the fan is running, it is pulling the
bathroom into a negative pressure with respect to outside. If there is
a gap around the fan housing or AC supply grille, it can pull air in
from the attic. It can do the same around a ceiling light fixture.
2) Make sure the exhaust fan has a tightly closing damper, or humid
outside air can leak back in when the fan is off.
3) Make sure the house is not under negative pressure. That will pull
putside air into the bathroom through the exhaust fan when it is off,
even if it has a good damper. Those things can leak!
Just some thoughts, because I have seen those problems before.