Eventually you should be able to make corrections (when you are over or under balanced) by altering which part of your hand is applying the pressure to the ground, instead of moving your hand.
A good way to make sense of this is to stand on the ground barefoot. Shift your weight around. You can shift more weight to the ball of your foot, the toes, either side and the heel. The same thing can happen on your hands, it's just less stable because we're less experienced at it. Hope that makes sense.
Really, read the Beastskills tutorial and practice, practice, practice!