I might be wrong, but it also depends on whether or not the mystery has next to it. Mysteries with can be activated whenever. Mysteries without will replace their basic attack and activate when its their turn to attack.
So, if you use Temari's Hurricane Jutsu which has , it can be activated and used whenever. But, if you use Ino's Mind Destruction Jutsu which doesn't have then that mystery will only activate when Ino would normally attack.