Ah, I've had a quick play and there is a subtle inconsistency when the station the trains heading to is already in its schedule. I've run four quick tests:
Depart to station not in trains schedule, exit train after it arrives: Temporary schedule applied, reverted on exit. Train departs back to original station.
Depart to station not in trains schedule, exit train whilst moving: Temporary schedule applied, reverted on exit. Train departs back to original station.
Depart to station in trains schedule, exit train after it arrives: Schedule is unchanged. Train remains at arrival station.
Depart to station in trains schedule, exit train whilst moving: Schedule is unchanged. Train departs back to original station.
That third situation is actually buggy as its supposed to always restore the original status of the train, so the intent was it would always go back to the original station it was at -- however, it does seem more like a useful accidental feature than a bug.
Leave it with me and I'll change the logic around so that when a train departs to a station already in its schedule, it will consistently wait there regardless of when the player exits.