Sorry it took me so long to reply. When ever you are getting odd readings from the carrier side, check the actual phone or phones. The phone is an independant meter of its data use. If your child's phone says it uses 6, or 12 gigs of data, then it did. Verizon should have a very close account, but may be 3 hours to days behind the phone. Date is NOT reported back to Verizon or posted on your account in real time. Data posted in the early morning was probably from the previous day.
Consider a faulty phone, app or user error. Factory resetting is not a bad idea. We had one iPhone that had to be factory reset regularly because it was not connecting to our home wifi. Don't know if the wifi antenna was faulty, but all other phone connected fine. Run away app... my sister noticed a significant drop in phone usage time and increase in data use. She looked at what was going on in settings and her weather app had gone nuts. Deleting the app solved the problem.
User error. Hate to say it, teens don't understand how to monitor and manage data. Settings should show how much is being used and by what. Set a monthly reminder to reset data statistics on an iPhone to match your bill cycle. iPhones also have switches in cellular settings to limit a phone to wifi only for some applications.
If you're happy with your existing plan, and don't want to change to unlimited, you have to take action on the phone, or kid to curb usage.
To be clear, no carrier can make a phone show it used more data than it did. Many people blame their carrier and insist switching solved it when what they did was change phones and that was the solution.