Appears one person got slung left in the turn and went out of the wagon, maybe from centrifugal force? Then the second person appeared to jump out after him. Perhaps second person also was sliding across the seat, jumped because he could not stay on the wagon, trying to miss landing on first person. Kind of a “crack-the-whip” effect with speed and sharp turn. Reins may have been jerked as people went out, changing right circle to left turn, then ponies doing a left turn back on the rail.
The other driver and ponies were really safe in the corner, first Team avoiding him. Then he decided to do “Roy Rogers” in running the other Team down, could easily have wrecked both wagons and hurt animals and people. Luckily he was not able to do that, so no wreck. Would have been easy to just let the loose Team go around until they tired, let them come to a halt without chasing them. Leaders appeared to know to avoid things, just really confused with no hands on the reins.
But in a crisis, there are always people who make bad choices, keep chasing the contained animals and making it worse. Comedy remarks were fine, but quit trying to grab the ponies! They just ran faster!! Hope it ended well, video ended too soon to tell.