the will usually turn directions with their butt toward you if they are fleeing you. It can be just a matter of habit, and not necessarily them flipping you the finger. its not so much which direction, but how they turn.
If they change directions facing you, it ususally is becuase you've got a better "draw" on them, so they are going around with at least one ear and eye on you all along, waiting for the next instruction, not just running away from you.
It doesn't matter to me if the horse , when stopping out on the circle, turns his head or even forequarters inward or stays put, as long as he does not COME IN uninvited.
if the handler asked for a stop, the horse should stop, and if the handler kind of freezes, so should the horse. If the handler backs up, the horse should draw to that. the horse looking inward is a kind of "what now?" question. Give it clear instructions right then. if you want it to stop and stand, stop your own body, and maybe , if necessary, put a little flip on the line to stop him. If you don't give him direction when he stops, he may decide himself to come in toward you, and you don't want him making that decision himself. you might want him to ask (turn and look at you, both eyes) but you answer with a direction , help him out.
ETA I just realized that I was thinking of Round Pen lunging when making the above comments. on a lungeline, you would never want him to turn AWAY from you.