I think self-analysis is intended as a mode for analyzing our games without the engine "spoiling" it for us — that is, telling us who is best in which position and what the best moves are. It shouldn't be starting at all, and the fact that it does start to analyze the position for us when we change the number of variations would seem to be a bug.
I could be misunderstanding your post, though.
Self analysis is acting weird lately. It won't start unless I change the number of variations and then making moves or cycling through moves won't update it until the number of variations are changed again.