The card states: “In between turns, place 1 damage counter on each of your opponent’s Pokemon."
So each time a player ends his/her turn, whoever's Dusknoir Lv.X is the Stadium, place 1 damage counter on each of your opponent's pokemon. It is not a body or power, and doesn't need to be stated (Only if opponent forgets). You do not use the Stadium's effect during your turn.