Did some more testing:

1. Sat in the car
2. Used the lock button to lock all the doors (all doors' lock indicator goes down except for the one I just replaced the actuator)
3. Manually pressed down on the lock indicator on the last door
4. Used the lock button again to unlock all the doors; all the doors' lock indicator goes up...including the one that was just replaced.

So it seems that the lock indictor won't go down automatically, but it will go up automatically.

Any ideas anyone?