The safest bet is to use it right after engagement checks are made and before dealing the shadow card. I'm not certain, but once the card has been dealt might be too late, as the enemy may already be considered to be attacking. At that point, it becomes a wasted card because what is the point of returning an enemy to the staging area after it has attacked? Now, you can't attack it, it's threat will count against you next turn, and more than likely if it was already engaged, it will be able to engage again.
I would say that as long as you don't start the combat steps with that Enemy (Choose it in part 1 of Resolving Enemy Attacks) then you could put it back in the staging area. Once you pass that point the Enemy is attacking and he have to deal with it.
In multiplayer the card the better because you can use it to change who a Enemy is engaged with because another player can engage it next turn.