What you are seeing is an adjustment to the ball coming inj not a push. The stride which I always had a big one but most teach to have a short one requires a shift and the back leg colapses slightly.
Once the front leg is down it just rotates as does the back foot. I always had as little lower body movement after striding as it set up the stable support of my upperbody as I swung the bat Too much movement makes it hard to make proper contact which is the most important thing when hitting a ball.
The back leg reacts to the force applied to the ball. The front leg is stationary and forms a 45% angle after impact giving you max power.
If you push off the back leg you will have problems with contact. The weight of the body is kept back.
Sounds a lot like pitching to me.
Tim doesn't push off the ribber. He has an abnormal stride wiich is 129% of his body height compared to most who are usually 77-85% of their height.