The video is a little messy and sloppy. I’m sure that’s partly because of my presentation skills being not as good as I would like. But I think it’s also because this particular situation actually is a little messy and sloppy.
For whatever it’s worth, my personal workflow to remove a single person from a group has become to do it from with the Edit Person screen. The process is clunky and slow, but it works 100% of the time, unlike doing it from the Groups tab in the left side panel.
I’ve been moving a person from one group to the other using the person list - click on person, uncheck group in left panel, check new group then click back on person name and take your time about going to the next person. That seems to make it stick but it is a bit slow.