I would be concerned as well if I was being charged for data overage when using Wi-Fi as the main way of using the internet. I am more than happy to help with this today!
If the device is an iPad it can use plan data while on Wi-Fi if the Wi-Fi connection is slow. This feature is called Wi-Fi Assist. This Tutorial shows how to turn off Wi-Fi Assist. Turn this off by going to Settings > Cellular data > Turn off switch for Wi-Fi assist.
If the tablet is Android simply turn off mobile data.
I’m glad I could help. Thank you and have a wonderful week!
Daniel, AT&T Community Specialist
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