The guide below will let you people help to force for app updates notifications on Windows Store live tile for the applications which are installed on your Windows 8 or Windows RT devices, because Store live tile does not show any notifications of app updates without setting it up.
Force App Updates on Windows 8 and RT
Access “Store” on your Windows 8/RT device and then tap on “Settings” > “App updates” options on right side of screen.
Click “Check for updates” button there and thats it.
Now, you will find Store tile on Windows 8/RT showing app updates for installed applications.