Try placing a signal at the end of the station after the track mark. This will force the AI driver to stop at the station if an AI driver is ahead. I think what's occurring is the script that controls the track marks doesn't have a chance to reset causing the train behind to continue on without stopping. I've run into a similar situation with stations when trains follow behind. My resolution was to put a dwarf signal at the end of the platform. In some locations, which eventually led me to do this all over, I had to place a signal before the station as well after when an AI train had the station and another followed. This forced the following train to slow down, if not stop altogether before entering into the station.
Now remember, this isn't 100% foolproof. There will still be a dumb AI driver that will proceed anyway but it's not as bad as a free for all which is what happens without the signals and this seems to slow down that behavior in most locations.