Because you can pick any player from any team as your twelfth man, it makes the biggest sense to use this booster in a matchday where we have many good fixtures - a matchday where many heavy hitters play against whipping boys. Basically, the best time is in a group stage where many crazy scores can happen.
You can use it on a player, that you do not want in your team in all 3 matchdays but on one matchday he has such a good fixture that you just need him in your squad.