It works without disengaging his hind quarters because you teach him to 'stop and not move a foot' whenever you take his head away. If you teach him this maneuver when there is nothing amiss with his world or yours, he learns very quickly that when he stops, relaxes his body and gives an inch more than you are asking for (he gives himself relief from the pulling rein) that you will reward him with a loose rein and will give him his head back.
If this is what you teach him, he will stop and give you his head instantly whenever you ask for it. Most horses will stop when you run your hand down the rein and get set for the stop. Since horses do not multi-task well and can only concentrate on one thing at a time, when you take their head away, you also take away the fear or reaction that you are trying to stop. It instantly brings their focus back on you where it belongs.
Personally, the only time I disengage a horse's hind quarters is when one is trying to take his head down between his knees and wants to buck me off. Then, I do not want him to have any power or use of his hind end.
The rest of the time, I do not want a horse to get used to 'throwing' his hip out when I take his head to one side. It proves to be really counter-productive for stock horses, reining horses, cutting horses and any horse that you want to 'hold their ground behind' and move their shoulders. It can be a very difficult bad habit to fix when a horse constantly takes a step out behind to get out of doing the more difficult move of bringing his shoulders around for a rollback or spin.