Small correction I'd need to make in order to make things more clear.
"tabbing out" doesn't actually do anything. Windows still runs it as if it was in the foreground. To be considered "background" it needs to be minimised. That doesn't make anything else false nor any less precise. It's just that if you want to try this, keep that in mind.
To know the app went in background mode, you can turn your speakers on. When the music stops, then the app went background.
Anyway,
My intervention is almost useless.
Btw, i'm very interested in talking with devs who got their games on XBox, in order to discuss performance etc. If any of you is willing to talk about that, just come in the Construct community Discord server, and I'll be happy to have a little chat with you.