Pinky,
I think, based on how it feels when I do it, the core comes in to play when you deliberately tap *lightly* as Cathe suggests. To keep your toes from slamming down on the top of the step at that fast pace, you need to control it from the core, kind of the same way you use your core during the "bicycle" movement in her ab routines.
I hope this makes sense. I agree that the legs work very hard, but if you focus on tapping very lightly and quickly, the core should come into play, too.
Sandra