Looking over the door-in-door patent 411669, it’s apparent the smaller door is not an emergency door. It’s simply a door that allows access to the boltwork, one of the goals being a door (or two) with no spindle holes or boltwork holes. It’s fully automatic, being operated by time locks and a boltwork motor (but only for the small door).
Normal operation is as follows.
To open the door, you first have to wait for the time lock on the small door to trigger the bolt motor which then allows you to open the small door. In fact, the inventor suggests using a stock Mosler door (patent 153348) for the small door. Once the small door is open you reach in, grab the operating handle, and retract the big-door boltwork. Unseat the main door using the pressure bars then pull open the main door. You probably want to close the small door so it doesn’t hit a wall as the main door opens.
To close and lock the door, first close the main door and seat it using the pressure bars. Reach in and operate the boltwork handle to lock the main door. Set the time lock(s) on the small door and wind up the bolt motor. Close the small door and let it lock itself.
So, again, it’s not an emergency door, but technically it is a “door in door”.