So the passenger car would be leaving whether people are fully on or not? What happens when the train is coming but the passenger car is not ready?
It isn't difficult to implement control systems, just like in every automatic train-style transport system, where... everything closes up in time prior to it being OH SHIT WE HAVE TO GO NOW time.
Doors automatically close at a certain point (where the train is a certain distance away, triggered systems removing human error from the equation). The doors are closed and locked for X amount of time, passengers sitting and giving time for the OH SHIT I MISSED IT people to clear the area. Then WHEEEEE! as the train-catching-car maneuver begins.
Same for the departing passengers from the moving train. Stairs for boarding open up basically LONG before reaching the next stage, basically right after
that car is docked on the train. New passengers board main train, next stop passengers board the recently-docked car. Stair access locks after a certain point, a good X amount of time prior to the car detaching.
If people miss, people miss. The schedules and access times will be strictly controlled, and information made readily available, so mistakes in boarding/departure are strictly on the person making the mistake.
Just like at subway stations were idiots fall onto the tracks. It happens.