Answer: The cup should have water in it all the time unless the plant is growing in potting mix, so you would not have overfilled it. There can sometimes be a problem with fungus or bacteria growing in the cup if light levels are low, the air is stagnant, and/or the cup is not being rinsed out periodically. Rinsing can be difficult to do when there are multiple plants on one support, but it helps reduce mineral build up as well.
If rinsing the cup clean and improving the air circulation (and possibly also gradually increasing the light levels) does not solve the problem, consult with your local Cornell cooperative extension for a more specific diagnosis. Based on knowing that they should be able to recommend how to treat it. If a chemical control is needed, they will have the most up to date information on what to use and how/when to use it for maximum results.
I should also mention that if your plant has bloomed, this could be part of the die-off that follows blooming. If so, it is going to die back -- the mother plant naturally dies off and is replaced by the surrounding little pups or offsets.
Good luck with your bromeliad!
Q&A Library Searching Tips