YES! Hah. I figured I was the only person in the entire world playing Football Manager on Linux.
Although, I have to say, I'm running mine on Ubuntu 14.04 on a Chromebook Pixel 2 with Crouton, in full screen, and I can ALT+TAB without any issues, so I'm not sure what your issue might be I'm afraid. There's no Crouton edition of Ubuntu 15.10 so I couldn't try it.
You can check your Ubuntu error logs to see if there's any clues. Apart from that, the obvious thing to do is make sure you're running the proper graphics drivers for your graphics card and they're up to date.
You could also try "maximised borderless window" in the graphics preferences (if that option appears for you).
Although, as far as serious problems go, and if none of that helps, at least you can still play in almost-full-screen in a window!
