In that video the only reason this boat capsizes is the lack of speed for a jybe in the given wind conditions. To jybe safely you need to aim to be as fast of the wind or even faster all the way through the jybe: In short, go faster!

I used to jybe slowly and gradually, limiting the angle on the tiller to avoid stopping the boat. I no longer do that, I now pull hard and crash jybe very quickly preferably right in a gust when I feel I reach the top speed I can get from it: the time spend in the go-slow zone is minimal, I don't lose that much speed and by the time the jybe is done I have enough of the gust left to pick up speed again.

Not to mention that the spi doesn't have time to flap, it goes from one side to the other in one big swich/bang noise, and when really well done (very rarely!) the telltales on the spi do not stop flying at all indicating that I was faster than the wind all the way through the jybe.

And you should leave your traveler centered downwind. The only time you need to let your traveller go away from the middle is when you drift waiting for the start or if you have to do a tight reach in strong winds.