Well I did say that I was having to imagine how it would work from memory, I can't check how this would actually work on phase II tuners until I get back from work - It's 4PM where I am.
Assuming that the phase II work how every other machine head works, only with a locking screw through the winding post - If you thread the string through the hole with some slack in the string left, then clamp the locking screw to secure the string, you then have to wind the excess slack around the post. Generally, when you wind around the post, every completed turn sits below the turn before, thus reducing the height of the string in relation to the nut. Exactly how using a string tree increases the break angle of the string in relation to the nut.
I think we must be visualizing and describing different things as to me this is plainly clear that adding extra wraps around the post and winding the string down as you do it increases the break angle to the nut. Now whether that is in any way advantageous to do I can't answer, I only offered it up as a possible motivation behind the practice.