I've got the Paintbox and several of the smaller ones. I tend not to use them often because the inks take so long to dry but when I do use them, I pull out the individual colors and use them. I'm not sure if I've tried to use the whole pad at once.
Melissa, I think you would be fine (i.e. won't contaminate the pads) if you press the stamp straight down on the ink pad, and don't wiggle it.