Select Monitor for Game Launch in Dual Monitor Setup

How do I get Lutris to launch games on my secondary monitor instead of my primary?

I’m suspecting this may be a complex issue for the following reason: If I launch Starcraft II, it will launch wherever I have my mouse pointer active. But if I launch Overwatch from the same instance, it completely ignores the cursor position and launches in the primary monitor. But maybe not! Perhaps there is a global setting on Lutris I am not aware of that overrides games’ internal settings.

I don’t want this question limited only to the scope of a single game, though. It’s more of a global question.