That is actually an older pic of the AVR and I have since changed it to 120vac, I did try putting a load on the generator and the same issue occurred, the only difference was that the inverter stayed charging a tiny bit longer before it kicked back to inverting.
So further testing ensued, I brought out the Harbor Freight 3500 and tried it, it worked for a few minutes but was heavily loaded until the circuit breaker on it kicked out. I reset the circuit breaker on the generator and tried again, then looked at the inverter screen and found the inverter was charging 13.5vdc @ 105amps and powering the shop lights at roughly 22amps , apparently the load on the 120 side was over 20amps as it kept tripping the circuit breaker. After noticing this seems to be a load issue, I returned to the powerline and realized the Kill-aWatt meter is only rated to 15amps and I was pulling in excess of 20amps through it, certainly not helping. Disconnected the kill-awatt meter and tried again, this increased the time of the cutout but still not working properly. These tests showed that the issue was not entirely due to my Powerline's output as the Harbor Freight generator was having issues too.
After all of this I finally read the manual on the inverter today, as it turns out there are a couple important settings that can create this issue, first as Mobile-Bob mentioned, you can set the width of tolerance on the incoming voltage & frequency, I had not done this so it is probably set too tight for the generator. Second important setting is the breaker size, pretty sure I have it set for 30amps, which would be a setting for a 3000watt+ generator, according to the manual the charger will adjust its pull on the generator based on this breaker setting.
All of my gear is located at my up north property so I will bring the manual next weekend and try again but this time changing the settings so I don't pull so much power and widen the AC tolerance and see if it will behave.