I watched the video where Tom demonstrated sliding the hips like they're on a rail, depicted by a training stick in front of the feet that provides a visual for the "rail".
This is probably the trickiest part of the S&T swing for me. The reason why is at address, this recovering conventional swing guy is still getting used to starting with more weight on my lead foot, and I'm also not used to ensuring my left hip is against an imaginary wall at address. Therefore, from that position, I already feel "left-weighted". Thus at the top of the backswing, it feels like I'm "as left as I can be", therefore it's hard to think "slide more left". There's no doubt this is what the pros do on the downswing, but wow is it hard to execute because the movement feels like it takes 5 minutes so it's easy to get antsy and curtail the slide to a slight "bump".
I snapped this pic from Rob Cheney's video about hip movement. I think Tom would agree that Rob is also a great S&T teacher, Check out the left hip at the top. It's moved forward quite a bit at the top, thus on the downswing the hips appear to be "pre-set". It seems this would make the slide (lateral movement) easier to accomplish. The feet diagram at the bottom shows how the weight stays on the left side. I would have dots on the inside of my right foot heel (at times) which would be incorrect. Plus, look how FAR the hips have traveled. Yikes!
I wanted to add another thought in terms of training.
This morning I got to thinking "let's check this out...the feel vs. real" thing. So I got in front of a mirror and took the club to the top, not looking in the mirror. Then I slid my hips as far as I could WHILE keeping my head in position, moving the club down into impact position. It felt like my hips were way out in front at impact. Then, I looked in the mirror and saw what looked like the guys on TV in terms of hip position at impact. Mirrors are invaluable to check my swing positions, and now I know I'm still far away from having a proper hip slide on the downswing. That said, I also know that a fairly lengthy slide of my hips is entirely possible. I simply never connected the real vs feel in the mirror.