That "T-Zero" that was displayed was not a change to your network.
Since iOS 9, when you switch directly from one app to another, for example by tapping a link to the App Store from Safari, it will show the previous app in the top left corner where your network would normally be displayed.
If you tap on the T-Zero up the top left it will bring you back to that app. It's there for quick multitasking — it does not affect your network settings at all. It just covers the area where your signal would be displayed. If you navigate elsewhere (such as by going to the home screen), or remove the app from multitasking, your network status will be displayed in that area again.
Apps cannot change your network settings like that unless you're using a jailbroken phone.
