Its an option for when they're not on their side. Instead of dumpin 'em , you can slide under and capture, then arch and squeeze crunching his head toward his chest. This will help finish the choke. Im sure his squeeze is amazing though, but ive finished this way as well.
so its like a japanese necktie where you hip in (forcing his head to his chest as you mentioned) but you go to the full darce grip instead of just sticking with the vice-grip?