I didn't see him do that, but I noticed last week watching the highlight videos from when he was contending in Detroit that he finds something to tamp down after every time he sinks a putt or taps in.
Since he must know that he can fix/tamp down spike marks and ball marks before the putt, I thought maybe he thinks he puts too much weight on the putter when he leans over to grab his ball, and he's just trying to even out that spot. It's pretty clear, though, that isn't the case either.
That's a decent drill for you, yes. Look at your left knee through impact and early follow-through. It never really extends.
Those are related. If the hips stall the clubhead overtakes. You are doing more than that, though, too, but that's a part of it.