I also have slight hiccups with my tenkan. I have a tendency to pull, keeping the force of the turn in my [tensed] arms and shoulders rather than connecting with and moving from center.
What has helped me is a slight inward rotation of the hips and a simultaneous inward curving of the wrist that is being grabbed - this creates the kuzushi needed to initiate the now blended turn from the hips. I've also found staying relaxed through all of this is likewise of key importance (ki importance, heh heh...)
The video is a very good choice, and gives something to think about in regards to the initial step-in/step-behind. I've never really considered that aspect of it, thanks for posting it!
Good luck with everyone's tenkan!