Thanks for the suggestion, but unfortunately that didn't solve the problem. I killed all apps on the iPhone, put it onto the snap-in adapter, launched Spotify, and started a song. After about 5 seconds, the music stopped and the play/pause button changed from || to > as before. This time, however, the iPod app did not start. I pressed > and normal playback continued. So the iPod app running does not have anything to do with the underlying problem.

When I disconnected the iPhone from the adapter and then launched Spotify, the problem did not occur. Thus it seems that the issue lies in the way the snap-in media adapter comunicates with the iDrive.