The door phone DOES have an adjustable timer that will automatically hang up the unit after the preset time has elapsed (15 seconds to 2 minutes).
Well, there were so may different versions and manufacturers of that door phone that Avaya used that I'll take your word for maybe ONE having that ability. At any rate, I believe all will automatically hang up AFTER it's answered and there is a period of silence. Probably what you are thinking.
Connecting the door phone to a hot line is only going to do what you are experiencing. If the IPO can't provide a door phone function, that controller will.
-Hal