I have experienced the same problem. I switched from Sprint with unlimited data and have yet to adjust to this outrageous bill for data.
We have the same problems. 6GB per month for two phones; wifi at home and both of our jobs. If we don't regularly turn off cellular at home, Verizon starts hitting my husband's phone every six hours with data charges (almost a GB yesterday morning when he wasn't using the phone). If we turn off cellular, it stops, but then in another month or so--once we've stopped turning off cellular so often because the charges fall off--the charges start hitting every six hours--and hitting during times we're actively using the wifi connection to text, etc. I use my phone--and data--as much as my husband, but my monthly usage is usually around .4 GB.
IT sounds like the phone is not using wifi. Go through your settings to force apps to use wifi.
when you open settings, mobile data, scroll down to apps. You can tap each app and restrict background data.
if there are specific apps running high, I can suggest how to restrict data use.
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