what battery is used for starting a generator in a class C

I had a 2006 Triple E and it had a two way charging system on it. When the coach was plugged in, the system charged the chassis, and when the chassis was running, it charged the coach.

Yours might be like that, and when you ran the motor the voltage to the coach was high enough, so your generator started.

Check your coach batteries with and without the engine running to see what the voltage is. I believe the generator should start from the coach batteries.