The latest iPhone iOS has a "security" feature which randomizes the network MAC address of the device. If the "pause" feature is based on device MAC address, you will need to turn off this feature in the iPhone so the MAC address of the iPhone stays consistent.
The iPhone also has a hotspot feature. If the kids turn off WiFi on the iPhone then the iPhone will use the cellular network connection. The kids could be turning on the "hotspot" and connecting the Xbox to their iPhones' via "hotspot". This will end run around your WiFi "pause".
Long story short.. unfortunately you're going to have to educate yourself on the various parental control features of the iPhone and Xbox to limit use. The "pause" feature in conjunction with the parental control features can achieve your goal.