Normal for onan 12.5kw to die when coming off shore power?

While I do not disagree with Mr. Wizard, I would do it slightly differently. A minute after starting the generator, not five minutes, I would start one AC. A minute later the second AC and at three minutes the third.

If it's really cold out and you are going to need the generator then I would give it 4-5 minutes before putting a load to it.