We have exactly the same problem. The phone is downloading hundreds of megabytes and using up all the data allowance and then the prepay credit.
Google Play Store was originally set to 'Wifi only', now it's 'No updates' but this behaviour continues.
I suspect it's the update to Marshmallow. We have 'Data connection' turned off but it seems the phone just ignores that and downloads anyway, even when a wifi connection is available.
Frustrating!!
Edit 1:
System update > Auto-download was also set to 'Do not auto-download' !! But my daughter has seen at least one system update recently.
On checking updates, system was 4.21.40.174, have just enabled wifi & updated to .184
Edit 2:
I found 'Data Usage' under settings, which shows both cellular & wifi usage for the last 3 months. It seems that Android updates are not the problem. There have been 100s of MB of cellular downloads from the likes of Youtube, Color Switch (what the heck is that?), Facebook, Snapchat, Pinterest, Chrome, Google App, Twitter - all of which are only used at home under a wi-fi connection (or so we thought). These same apps also recorded gigabytes of data under wi-fi (which makes sense, but why the cellular as well?)
As I said, data is usually turned off unless wanted (Pokemon Go, anyone?) and updates are wi-fi only.