Hi,
My Yamaha 3000 Sieb when new did not "like" to be loaded. It would sometimes flip the internal breaker which mean starting it over again. After 20 hours run time that was much less of a problem.
Now that I use it with the Magnum inverter, power is not turned on inside the RV for some time. I know it is a short time--but it seems as if it is ages.
I think I can safely say that starting an inverter generator should be done with the economy switch turned off.
My own procedure is to have no large loads turned on, start the generator, wait for the Magnum to allow pass through, turn on load support on the inverter, then switch the generator to economy mode, and turn on large loads such as the air conditioner. This is easy as pie for me as I have a Pinella remote start for the Yamaha. The Pinella allows me to move from regular to economy modes remotely.
Shut down is:
remove large loads
set economy mode off on the inverter
shut down the generator