@adityapstar is the second monitor plugged via just one USB-C cable? Sometimes these will use DisplayLink which puts f.lux into a different mode that is not always as capable. However, your "driver info" seems to say it should be working as a native device. If you have a spare HDMI cable, I might try that instead to see if it behaves better.
One second thing to try is to see if the second monitor can be disabled with the "Disable" menu, which makes a list of monitors. Since you said sometimes it does disable (without the fade) I would expect this to work, but I'm curious if it works with the games as well.
I suspect what's going on is we are not seeing these games as "fullscreen" which would be a bug we should fix - can you say which games show this?