Video with just Nagato and Main character vs Kakashi clone
Would be nice for this. Set to auto battle.
Auto battle should trigger any available mystery skills BEFORE they use standard attacks.
Nagato not being prompt mystery means that he will wait until it's his turn to use his standard attack BEFORE using his mystery IF it has already been activated.
IF he uses standard...then mystery is used....All ninjas will attack...then all ninjas will attack the 2nd turn UNTIL it's his turn to use his standard...then he'll use mystery and THEN use standard.

Kind of annoying, but we can better see it if posted as a video/gif.