Jacki, You are entirely correct. The inverter will carry the frig. TV and some lighting for a considerable time prior to automatically starting the generator at which time it will run 2 hours or more to fully recharge the batteries.
Now, one thing to check. Make sure the inverter is on. It is very easy to accidently turn it off while setting other items on the touch screen.
You want to make sure the inverter is on, the charger is on (when power is present or the genset is operating) and the auto gen start is on. Always take your time after resetting any of the value to verify all preferrences are still on and correctly configured.
Peter - Doctor of Mixology