Google → [Tablet] Polaris Office

My wife's SM T110 Lite has this on it and I have turned off as the only thing it was needed for was opening PDFs and she uses Adobe Reader for that.

The problem is although I have turned off and auto-updates in the play store turned off it keeps updating on start up every now and then. It acts like it is downloading the whole 45MB rather than just an update.

PO is not the only one that does this. What is the best way to stop these unwanted intrusions?

Maybe it's doing some sort of cloud sync? Anyway, with root access, either freeze it with Titanium Backup Pro or a similar app, or block it's wifi/cellular access with a firewall like AFWall+. There are a few firewalls that don't require root, but I don't know how well they work.