My son's iPhone 5S is using data with while on a strong wifi connection. Its caused us to go over on our att bill. What setting does he have on that might cause it to override the wifi connection. I had him turn off all of his cellular data connection in his apps. Most of the data usage is happening while he is asleep. The phone has been in my room so I know he is not using it.
WiFi is turned off when the phone goes to sleep to preserve battery, unless the phone is connected to power. So if there are any background apps they will use cellular data when the phone is asleep, unless the phone is plugged it. So one option is to leave it plugged in overnight. This will not harm the battery.
The other thing to note is that the timestamp associated with data usage as shown on the bill or the AT&T website is the time that cumulative data usage was reported to the billing system. That usage could have occurred any time in the previous 24 hours.
If you want to track usage and when it occurred go to Settings/Cellular and note the data usage, then check again later. In your case you might do this at when putting the phone down for the night, and again when you get up in the morning. You can also see which apps actually used the data on this page.
iPhone 5S using cellular data while connected to wifi
