Iphone Mirroring

One of the requirements for Screen Mirroring (AirPlay) is that both devices, your iPhone and your Apple TV, be on the same Wi-Fi Network. This means that your iPhone and your Apple TV will drawing data from your Wi-Fi Network and not from your Cellular data.

Axel F.

For streaming a video stored on the iPhone, it would happen over a Wi-Fi connection to the Apple TV. For streaming a video from the Internet, the Apple TV will open a direct connection to the Internet source ... as the Apple TV is being "authorized" (by the iPhone) to access this source and no actual streaming occurs between the iPhone and the Apple TV.

... so it will depend on how your Apple TV accesses the Internet ... which typically will NOT be via a cellular data connection.