Agree with Ron, the Onan on our rig will not provide power to the rig until it has run long enough to stabilize. That is 30 to 60 seconds at least, you can hear it run irregularly for a bit, then stabilize then run different when the power is turned on. After that the Progressive Industries EMS takes a bit to analyze the incoming power and only after it is satisfied does it make the switch, which can be heard with a noticeable 'clonk' as the contactor is engaged. I've never timed the whole process and I don't think it is quite 2 1/2 minutes on my rig but its not a lot less than that.
Taking precautions by turning off the A/C and other items in the rig before starting the generator is not going to hurt anything but if your generator is modern it already has safety features built in for that. There also seems to be a delay in the A/C coming on after 120v is provided. The A/C definitely does not start immediately. Perhaps that is a newer feature or a different thermostat but it takes another 2 or 3 minutes after the 120v is supplied before the A/C comes on in my rig.
Turning things off before disconnecting from the post is not required, but it makes good sense to not unplug when there is significant current flowing as that can arc and eventually burn your plug contacts. Or the receptacle contacts on the post. I suspect many post problems are actually caused by campers pulling the plug when the circuit is loaded thus arcing and pitting the contacts. Over time this degrades the receptacle and increases resistance and the heat produced in the post.