I agree that TTB is supination. I think the alternative is radial/ulnar deviation that is more like a karate chop.... which necessitates the instruction to stay inside the ball....and often results in back side flairs from dragging the bat by the knob.
Learning to TTB fixes all of that.
Yea, folks that struggle with swinging down (Bobby Tewks) to the ball never put themselves into a leveraged position so the hands could be pulled vs pushed, so they ended up chopping down on the ball out front..
Hands being pulled by the core.