Good point. I may just start keeping a little glass jar of water handy.
Usually, if it was a particularly dark color, I shoot just a bit of of tamiya thinner through it (after the windex) just to make sure it's really clean.
I used to use just tamiya thinner, but then I realized 2 things; 1) I was going through a lot of thinner and windex is cheaper and 2) windex actually does a better job of cleaning up acrylics. I don't know what's in there, but it really got out some old stubborn stains from the paint cup.
-Fred