What you should do to avoid this is to manually sync (CTRL + ALT + G on pc or use the sync button in the app menu) and then close the app or browser tab before switching to another device.
Also, if you are just struggling with the arenas from your phone, please note that you can start the arena game on your phone and then continue that game from pc without having to open the idle page on pc.
The MP dashboard (
https://www.warzone.com/MultiPlayer/) will have all your MP games listed, including your current arena games.