In my opinion, a certain threshold for this ability is a must. Completing the map is one, a certain level is another. Third is the one I suggested, a certain Team Power number vs. difficulty of the monsters.
I think Team Power vs. monster difficulty is the best, because it is what really counts. You absolutely cannot fail, if you have high enough TP, regardless of advance in map or your level. Small Giant has already a way to calculate this, because you do have recommendations of TP level in Quests.