Co-op multiplayer on Apple TV via Arcade

Hi. I've recently started using Apple Arcade on my Apple TV. I've connected a PS5 controller, it works and all is good.

However, when I try to play a co-op game by adding an additional PS5 controller (e.g. Sonic Racing or TMNT Splintered Fate), I just can't seem to find out how to add an extra player... The two controllers are connected to the Apple TV, I just can't play with more than one player.

There's obviously something I'm doing wrong, so I hope someone can help me :)