The cup isn't as important since the water in there shouldn't be going back into the tank anyway. It all depends on how anal you want to be. Some people won't let any tap water into there tank and would say for a newer reefer to not do that because the skimmer can over flow into the tank while you are learning how to set it up to just use your ro/di water to rinse it and not use tap water. That being said. I wash mine with tap water and a paper towel.
I rinse all my equipment with my 150ppm tap water and haven't has any issues thus far. Some stuff like foam guards and prefilters I'll sometimes wash in RO water.