Same is true of most UPS outputs, those recep testers don't read accurately on them. They often show reversed hot/neutral. We had a customer complain a control panel outlet fed from a UPS was wired backwards because he tested them with one of those testers.
The GFCI testers work on the fact that neutral is always bonded to ground. So you have 120v from hot to neutral and hot to ground, no voltage from neutral to ground.
Those little inverters have 120v but it is something like 60v from hot to ground and 60v from "neutral" to ground.