Topbonus is a completely separate entity from Airberlin (it is owned by Etihad Airways) and sits only on the interface between topbonus customers and the various oneworld, Etihad Airways Partners and other partners that topbonus deals with.
You - as an AAdvantage customer travelling on airberlin - exist entirely outside the topbonus universe. It is in no way responsible for "distributing" miles to AAdvantage customers who happen to fly on airberlin, just as AAdvantage is in no way responsible for, say, distributing Avios to BA customers who happen to fly on AA.