So, tonight I made a conscious effort. I started the car as I walked across the parking lot at -10C so it would warm up about a minute. When I got to it I unlocked the hatch with the fob and dropped my stuff. I then unlocked the driver's door, again using the fob, and the car didn’t shut off.
I suspect the anti-theft feature of the remote start isn’t integrated with the auto-recognition feature of the door lock. If you get in without “manually” unlocking the car, it thinks you’re stealing it.
Now, I wil try this again when it warms up to see if temperature has any impact.