Chris' site shows still images (unless you've updated it recently, Chris) which cannot show the entire story. Stills can show things like hip/shoulder separation at one point in time but that's it. You need video to show the timing, tempo and smoothness of the full motion in context. Send me a PM with an email address and I'll send some video to you.
Dick used to say that the front foot should land before hip rotation occurs but he's well aware that it doesn't really happen that way. He typically is trying to communicate to people in a way that he believes will get them to do what is required, whether the terminology is absolutely correct or not. My opinion of Dick's intent only.
The hips must rotate INTO landing. The pros all do it. The shoulders must NOT rotate until the front foot lands. All of this sets up a stretch across the torso which, if timed right, allows maximum contractile force for shoulder rotation. Since the shoulders rotate immediately upon landing, the hips MUST rotate before. The key is that the hips do not rotate too early. They must do it very late.
Also, no herky jerky movements here with 2 phases. You don't want to rotate the hips, pause then rotate the shoulders. The energy transfer is lost then.
Just lunge sideways and, at the last moment, start the rotation phase by with the hips. Use the back leg to assist in this by spinning that back foot over. You might want to think of it as a "rotational push" very late.