It is used before the mission success/failure is announced. It has to be used before the mission result cards are “shuffled” so it has to be used before they are turned over. So once you announced success (or failure if that had been the case) it could not be used. The moderator should query the card holder(s) before announcing the results.
That said, it doesn’t hurt for the player to remind the moderator that they might use it during the vote process.