Organizing and accessing contact information in Outlook.com
I actually solved my own problem. I got so frustated that I just stopped and left the iPhone as it was configured. The next morning when I woke up the contacts were there.
I don't know why, but the sync seems either to take ages or just happens very infrequently. At least there is no indication if it is syncing or not at all and it also seems that this is not an incremental sync but rather an all-or-nothing approach. Strange, but data is now there.
Perhaps some patience helps others as well.