After doing a couple more battles to verify, no Trick Room was used, and I don't have any hold items. Shuppet has a base speed of 45, and it still outspeeds Gengar (Base 110), my Grovyle (Base 95), Pikachu (Base 90), Meditite (Base 60), and Kirlia (Base 50). It's almost like when it gets sent out an automatic Trick Room gets put up, so either Shuppet got a massive buff to speed or it's bugged to put up Trick Room when it gets sent out.