Sorry for the monologue, but this might be useful for someone that may face this problem in the feature.
After being more attentive to the network usage pointed by Network Monitor Mini, I think I found the culprit.
I've spent the last weeks with mobile data completely off, using only WiFi, yet on a couple of occasions I noticed Network Monitor Mini reporting minimal network usage being made when no know network WiFi was around.
As the screenshot shows, the WiFi is not connected to any known access point, yet some data was being uploaded by one of those processes.
I think the phone is trying to ping the cellular antenna for a location, thus accounting for mobile data access.
I've disabled the location and I will keep monitoring the data usage to see if that is the real culprit. Also noticed that Network Monitor Mini has a traffic breakdown mode per interface. I'll use that to distinguish wifi and cellular data.