I think the alt. light is designed to have 12V from the battery on one side of the bulb and 12V from the alternator on the other side. There is a shunt to provide a ground circuit. If the alternator voltage drops it allows the battery voltage to ground through the shunt and lights the bulb. If the convertor is providing power to charge the chassis battery with a BIRD system, or similar, and it is higher than the battery voltage, could light the alt. light. I would try running the engine while plugged in to shore power and see if the light comes on. Also check the AC voltage from the generator and DC voltage from the convertor when plugged in and also with the generator. Maybe the generator is to high.
Just my 2c.
2016 Wildwood 28RLDS
2014 Tundra 1794 Platnum,"23" T-Bucket
2011 Harley Softail, 2010 Spyder RTS