You are running in Windows mode if a program in the background ask for attention it will get it. If you want to tile clients on the same screen this is part of the sacrifice. if you want to minimize this issue than hide your taskbar or shink it to nothing. This will not stop popups like from virus scanners or taskbar notifications. You can turn some of that off but nothing is perfect. I get prompts from Skype all the time if I did not want to see them anymore I would kill skype. You can set your windows to always be on top there are work arounds none of them are sexy.

If you are running your other 4 clients on a different computer than you can just go full screen on the main computer and just Alt-Tab out to your browser.