You are in a "worse spot" with your generator.
1....Generator "ratings" are often "imaginary". That is, it's easy to pump up the numbers (it's just a label) to make things sound good. But regardless of that, somewhere buried in there the gen specs should show what it can "start" in the way of motors
2....Big motors such as your compressor have a VERY heavy starting (surge) load. This is especially problematic when using a generator
3....Make sure the compressor is "unloading" properly. In your case you MAY have to rig up something "special." Maybe some sort of time delay to allow the compressor motor / pump to get up to speed before it starts working against a head
Unloader systems vary. Some are a "tell tale" little separate tube going to the switch. This pops a little valve to relieve compressor cylinder pressure on shutdown
Some unloaders are built into the check valve going into the tank. These are fairly UNreliable, as they can stick
Some unloaders are a mechanical, such as centrifugal device on the compressor with a mechanical link running up to a head, to actuate a valve. You need to see if these are working
"Clues" are hissing on shutdown, and with the compressor unhooked (disconnect pulled) you should be able to "easily" turn the compressor flywheel, should not feel the cylinders working against pressure.
I would go through the compressor literature AND the genset literature carefully. Find out if the genset can actually "start" the compressor, and make certain the circuit size is 'up to the task.'
Did you say this is a 30A breaker feeding the compressor? No12 is too small for a 30A breaker. How long/ how big is the total wiring, IE from generator to box, and from box to compressor? Depending on length, no 8 from the genset to the box, and no10 from box to generator.
