^The way it is written implies to me that you should be able to be used during your turn as well. It is and stays a Trainer but with the current wording, one that can also be played during your opponents turn.
The second sentence states it will "Prevent all effects of that Poke-Power".
What Poké-POWER? The first sentence let's us know it is the POWER that one of your opponent's Pokémon is using on your opponent's turn.