Perlite, won't it float
 

If you're using Perlite, won't it float over the top of the cup when the water is entering the cups or is something needed on top of the cu?

Don't let the water go higher than the cups, then the perlite won't float out. Even grow rocks will float out of the cups if the water goes to high. That is what the overflow pipe is for, to control how high the water rises in the bottles.