My feeling is that AirTran can be quicker than most about closing the door early. They will claim in your situation to be following their published ten minute rule. Their records, from what you are saying, will show they closed the door exactly ten minutes early at 9:40 PM.
If I ever felt they were leaving ahead of the ten minutes, I would find the nearest AirTran employee (nearest gate where they have a computer), ask them "what time do you show it is?" and if it is more than the ten minutes I would take their name and the time that they gave. Then you would have the foundation for a complaint and getting some kind of customer service compensation.
I did this once for a Delta flight ATL-JAX and got some miles put in my account.
By walking around the airport and letting the clock tick down to seven minutes, you now have let them be able to say it the way they want to in order to follow their rules.
If she was on a tight connection, presumably due to an inbound delay, the airline should protect her fully including the overnight stay, even with them leaving early within or outside of their rules. This would be the same if it was ten minutes before or if she got there after the flight's published time--the inbound was late, end of story.
I don't think IDB would ever be an issue in this case; it is for when they don't honor your reservation due to overbooking.