The generator will start off of the coach batteries. You can always use the boost switch on the dash to get the engine batteries to start the genny if coach batteries are too low.
I recommend that you set the auto start at a higher voltage, like maybe 11.5 or 11.8 volts. If you wait until the batteries are down to 11 v they are pretty much dead. Discharging your coach batteries way down will drastically reduce the life and capacity of the batteries. It is recommended not to go below 50% state of charge.
Using volts alone to determine the power left in the batteries is a bit problematic depending on the load current at the time you're measuring the voltage. For example if they are running a light load of say 10 amps, the bat might read 12.2. But then if you run the microwave oven, the amps will jump up to 180 amps and the battery voltage could drop to 11.9 v.
This is all kind of a trial and error learning process. Lots of variables, most notably the age and condition of the batteries. There are battery level monitors that measure amp-hours and that gives a more accurate state of charge of the batteries. If you rarely dry camp, this isn't a big deal. But if you plan to spend 2 or more days off-grid a few times a year, then it needs attention.
I bought this bat monitor to protect my $1100 investment in 4 agm batteries: