Not sure why that happens, but you may want to try "borderless window" instead of fullscreen in the game options. If that does not work, you could try running the game in gamescope, or enabling the wine virtual desktop with winecfg (point it at your game-specific wine prefix, you can also run it from protontricks). These are just a few ideas, but it does sound like a mechanism that is part if the game, not wine. Just like some games crash when you alt-tab in windows; gamescope tends to fix that.