I always turn up with a Preisstufe B ticket (usually a 4 ride ticket) and I think the SkyTrain is included in the ride. Going back, it can just be validated in the orange or red box at the SkyTrain station in the airport. But I have never had a ticket control on the SkyTrain. Took me a long time to realise you had to pay, too!
If you were coming from Düsseldorf, then a Preisstufe A ticket would all that you need.