Have I got this right? Start up the engine on the appropriate battery, OK to turn to both or domestic only whilst running, but never to 'off' unless the engine is stopped!
Thats correct, but does depend upon your wiring set up..... so understand it properly....
What you are actually trying to avoid is having the alternator running without a battery connected, as that will damage the diodes within it.
Mine for example can be run with the switch in off, because thats how its wired....
So you are safe if the off position is avoided, but its best to really understand what connects to what in the end.... otherwise sooner or later you'll accidentally run both batteries flat....