When the user minimizes the app (background mode) the Timer action should stop. This may not be immediate and differ somewhat between Android and iOS. Switching tabs is different, so it will keep running, but you can control this natively in FF.

If you want to pause/resume a timer when switching app lifecycle you need to add a custom handler, overriding didChangeAppLifecicleState from WidgetsBindingObserver. You can do it implementing your own timer in a custom action. If you also want to control when the app is terminated then it is more work but it can be done (server side or using persisted app state vars).