I know what you're talking about. I vibrate my eyes like that sometimes to freak out my boyfriend. Probably everyone can do it, but most people haven't tried it, or haven't tried it enough to develop a connection between their intent and the muscles that do it. It's probably like being able to see one of those "magic eye" images, and anyone can learn to do it if they master the muscle control.

But I can say with certainty that this is quite different from the movement of our eyes during REM sleep. Watch someone's eyelids sometime when they're sleeping. Because the eyes are slightly oblong, you can see the movement of the eyes underneath. They roll around at an even pace, very similar to when we are awake and looking around, not vibrating at all.