I have looked at your site a little.
For your competitions (Wettkämpfe) you are using the main component displays. You have two categories:
Ausschreibungen und Veranstaltungen and Ergebnisse. Think you are using the List All Categories Menu Type.
For Ergebnisse, which shows the results of past competitions, the items list nicely with the most recent competition at the top.
For Ausschreibungen und Veranstaltungen, which are future events, the order is with the the one furthest in the future at the top. Think you would probably like that one the other way around with the next one to occur at the top.
There is a solution to this 'challenge' by using two separate jDownloads menu items: one to show Category Ergebnisse and the other to show Category Ausschreibungen und Veranstaltungen.
The Menu Item 'Single Category' shows the contents of a specified Category and its sub categories if there are any. The important point is that in the List Layouts tab of the menu item there is the possibility to set the Downloads order. So one menu could show in say Title Alphabetical and the other could show in Title Reverse Alphabetical.
Would that solve you present "challenge"?
PS will still look into the ordering in backend