It’s not really a hug but more of a hold, as in, to hold you in place and keep you calm. If you were to get too excited, turn around and see something that frightens you, or even turn around and see nothing at all (which can also be frightening/shocking), basically any extreme reaction to the situation, you would most likely be jolted awake and that’s what they’re trying to avoid. It’s really easy to fall out of that state, especially when you’re newer to experiencing it.
So it’s not a show of affection, but more of a gentle and firm hold that they’ll use to keep you still and calm enough to keep you in the state of being able to communicate.
As for the mantra, he could have been referring to this: