I just tried on my phone with a fresh install of Firefox, and I get the same error message.
Firefox must be trying to start in the background for some reason. Maybe to get notifications, sync bookmarks, or whatever. I'd suggest you ask them in one of their communities what their app is doing in the background.
I doubt you'll see it in any lists of running apps because Firefox may just start up quickly, do something and close again within seconds.
After disabling Settings > Apps > All apps > Firefox > App battery usage > Allow background usage
, I haven't seen the error pop up. It probably would stop popping up if battery saver mode is on, too. Firefox may request to run after the phone starts up, so it popping up after a restart wouldn't be surprising.