Further, when you change the From or To Room values in a schedule Revit will honor your choice and toggle the other to the opposite value. If you just flip the door in the plan view though the schedule does not change. This is intentional.
A door may need to swing into a corridor for exiting but technically belong to the room and therefore the To value should not change. This may be the exception to the rule but that's how it works.
I created a video that demonstrates this a bit. I also mention a limitation that was mentioned in a post about this at AUGI. The limitation is how thin a room can be before the door no longer can generate a To Room value in the schedule. The magic number is 14", in my testing, any thinner and no To value.
If you want to listen and watch here instead...