>>> Internet is switched off
Hmmm. Possibly but, then again, possibly not.
I used to have a phone where I could buy 'bundles' to get internet access. If I didn't buy a bundle I could have unlimited access for £1 per day. (i.e.it wouldn't matter whether I was using the internet for 20 seconds or 20 hours in any one day; it would still cost me £1 for that day's access to the internet). I wasn't buying bundles but, as I wasn't using the internet, I thought that my credit shouldn't drop unless I made calls or sent texts. However I found that it kept going down for no apparent reason.
I eventually worked out there was an app on the screen which showed me the current weather conditions at my location. (The app was pre-installed when I bought the phone). That app was periodically accessing the internet to supply my phone with the data, so I was paying £30 per month just to know what the local weather was like (which I could have worked out by simply looking out of the window anyway). The solution, obviously, was to disable that app.
So, even though your OH thinks that he's not using the internet, perhaps there's an app on his phone which keeps accessing it anyway, running his credit down?