The (original) rider seems to have gone for the method of peeing the horse off and sawing at it's mouth rather than training it to rear. I've worked with stunt horses before, and I can tell you now that horse hasn't be trained properly
Just up the road from me is The Devils Horseman Stunt Team. I have been to a lot of their shows and they do perform rears. Gotta say, they don't pull on the mouth at all, it seems to be voice commands, long whip and legwork with them.
That horse in the advert looks terrified. The tail swishing constantly, the ears flat back, whites of the eyes showing. Poor thing.