It should not matter, at least i would not think so. The skimmate being pulled came from the tank in the first place.
I guess if a concentrated glob hit the fish in the face... Then again, it takes a Red Sea skimmer a while to break in. You wouldn't see a whole lot of skimmate for a while. Maybe a light tea, but not the dark stuff.
Lastly, if the cup filled completely in one night, then it would have to be very watered down. I cannot speak on the size as I run an reef octopus. However, with all this said, I would venture to guess something else may be going on.
Might be one of those coincident things, just happened to happen when you added the skimmer but still unrelated. Either way, good luck, hope you get this figured out.
"When you're down by the sea and an eel bites your knee... That's a Moray"