I have a 2011 Mac mini server with 2 monitors. When I am online and have one monitor on full screen and do anything on the other the first goes back to regular screen. How do I prevent this?

I have a 2011 Mac mini server with 2 monitors. If I am online on both monitors, using different browsers on each monitor, and press an onsite button on one monitor so that I am full screen on that site, if I do anything online on the other monitor the first monitor goes back to regular screen. What do I need to do so that what I do online on one monitor does not interfere with full screen online on the other monitor, and or so that I can be full screen online onsite on both monitors?