Ah thanks for the catch! We've been only testing with a wired Xbox wireless controller so far.
In our testing, this bug also happens in offline versus if:
You take the first controller (controller 0) and set it as player 2 on the screen right before character select. P1 side by default is controller 0, and P2 side by default is controller 1. After setting the controllers though, both P1 and P2 are set to controller 0.