Normally, when I have apps on two separate monitors, I can switch focus to an open app (on either screen) using Command+tab. I can then switch spaces on that specific screen using Control-arrow keys. However, I am unable to do that: Despite the fact that the screen will focus on a specific monitor, I can only switch spaces on the screen where my mouse resides.
Switching spaces using the keyboard shortcuts is dependent on your focus, rather than the app that's in the foreground. macOS determines your focus by looking at your mouse's position.
If it used the foreground app to determine your focus, and you had a space with no apps open in it, you would never be able to use a keyboard shortcut to change the space on that monitor.