Messages can, don't don't always, move between nodes. For example, there is a configuration parameter "PrefetchSize" on the connection factory that tells the factory how many messages to cache in memory. A message that has been prefetched will not move between nodes.
Thanks a lot for the suggestion, Doug!
I have checked and indeed the prefetch size is set. I will try to repeat the scenario with having this in mind and verify with more messages than the prefetch size.