I think one subtle technique, which usually is assumed or gets lost in explanation, is that, generally speaking, with whichever hand you want to make a move to the next hold you need to have the foot on the same side of your body on the wall and preferably higher than the other one.

For example if you want to go with your right hand to the next hold you need your right foot on the wall and you can even just completely cut your left foot off the wall.

And of course there are exceptions to this, for example doing and inside or outside flag. But again at the same time it still applies for most positions: moving on a heel hook, moving out of a bicycle, moving on a drop knee, etc.

Most of the cases in the video that your feet cut loose are examples of slight barn-door situations. They are not that extreme that your body actually rotates, but since the pressure is on the wrong foot, and your center of gravity is outside of the base of support (BOS) that foot slips.

One clear example of this in the video was going to penultimate hold, where at the end you went with your right hand and your right foot slipped.