if you are asking about nagato,

the best time to use him is to cast it when he cast his immunity, that way he wont be acupuncture/immobiled which might cancel his mystery. If you wait for him to use his standard then only cast his mystery, his mystery will be brought to the 2nd round which are prone to be cancelled with acupuncture/immobiled.

depending on which enemy you are facing, in a case they dont have anyone that can acu/immobile either through chase/mystery then it is safe to have nagato mystery casted early/2nd round, again it always depends on who are you facing at that point of time.