I am not familiar with Win8.1 at all, but Win7 has those pesky "reminder" pop-ups that keep going like the energizer bunny once they start themselves.
I am sort of wondering if this is a flag internal to Windows to check for its "expected" monthly update, even though you are not online. Most Windows updates are non-invasive, and I have only had a couple over the years that I intentionally backed out of. More speculation here, but you definitely have one of the freakiest issues ever.
Based on your concerns with an update, an option is to create a system restore point manually, then put the computer online and let it update (manually run Windows Update). If anything goes amiss, you can 1) either restore manually or 2) uninstall the update from the updater utility. If you do need to back out of an update, you can also tell that updater to ignore it in the future.
If this truly is the updater itself, it is incredibly odd that more folks haven't seen it though.