Mr Silva must know that the joists from the opposite room will be adequately supported by his temporary structure. How they are supported, and for that matter how he knows ... is not in the video. It's a good question.
If you don't have that confidence ... if you think you have joists that end over the wall and that do not protrude past the wall at all, you can and should support on both sides.
It's easy to figure it out. A 1/2 inch hole in the ceiling and a $70 borescope will allow you to see the joist configuration and whether and how they are supported by the wall or by screws or nails into each other.
Also ... he seems capable of cutting open the wall very precisely, building the temporary support, and taking it down without doing any damage whatsoever to the ceiling. It's like he was never there. I'm not that good, are you? Because if you're going to have to paint, there's not much harm in cutting a bigger hole in the ceiling and sticking your head in.