Shared DE's are owned by the parent MID (_clientID) value so you would have to update it at that level.

You would have to plug into the Data Relationships on the SFDC side and see those connections better. I've done it many years ago, but haven't touched it in a while. So what is happening is that for whatever reason in SFDC the 'Affiliation' object has relationships to both Contact and User that it sees as 'primary', but on your 'Application' object it is prioritizing the User object relationship and none this is documented well in their Help section. Are either of your Contact relationship fields between Contact <> Application required fields on the Application object records?