Well hopefully we can get to the bottom of what a push is
It gets complicated because multiple muscles are involved with most movements, and muscles can only actively contract.
In reference to the Lorenz tee swing, I see the hands not connected with the turn of the torso, and getting well ahead of torso rotation. This is part of what I see as a "push" in a swing. Looking at the rear leg-hip-torso alignment, the rear knee is behind and "pushing" the hip, which is behind and "pushing" the torso. That knee-hip-torso alignment is quite a lot different in the game swing. IMO. YMMV.
It's certainly possible that the tee swing is a specific drill that is helpful to the cocktail of feels that works for her. Personally, I can only see prescribing that movement to a hitter to address an issue specific to that hitter's individual needs.