Just make sure that the two batteries aren't linked together when you start the vehicle otherwise that starter motor could draw from the second battery and pop the fuses or worse
i.e. most vehicles stop power to the ACC items when starting the vehicle, so connecting the isolator to an ACC powered wire should fix that issue.
Checking that I'm correct?
Well, since you asked...
If the batteries are a cranking type and a deep cycle type, the scenario you described is highly unlikely because a cranking battery has a lower resistance, so it would take something weird going on before the deep cycle was providing any significant power to the starter.
That effect becomes even more pronounced if the charge wire to the aux battery was something like #10, which adds even more resistance.
My truck has a dumb solenoid, ignition controlled. When I got it, it had #8 between the batteries and a 50a fuse. Starting the 460 engine with the solenoid engaged never popped the fuse.
It was like that for decades before I got the truck. I replaced it with a chunk of #4 battery jumper cable and got rid of the fuse, and then later replaced that with 1/0 welding cable. I upgraded the wire to max out the amp flow for bulk charging, not because the smaller wire was a problem - it wasn't.
Also, using ACC to control the solenoid instead of IGN is not recommended. The batteries should be isolated whenever there is no charge being supplied.
(Self jumping being an exception to that rule, but also an unusual occurrence.)
Having dissimilar batteries tied together during charging us fine, but keeping them tied when they are not being charged is unhealthy for the batteries, and using ACC would have them tied whenever doing something like listening to the radio with the engine off.