I don't have the time to construct the entire query for you because your fields are not identically named in the two queries and I'm a little busy right now but here is a start for you.
Use this as a template that you can build on:
Create a Query and select all the rows from tblMasterDap that will receive data from tblPublications.
Then go into SQL View [View -> SQL View] and add an INSERT INTO row that contains all the fields in tblPublications that have data that needs to go into tblMasterDap.
The fields in the INSERT INTO row need to be in the same order as the fields in the SELECT row. Access will match the field names by the order in which they appear in the two rows in your SQL and append the data accordingly.
Code:
INSERT INTO tblMasterDap ( [Pub ID], [Title/Subject], [Media Tier] )
SELECT tblPublications.[Pub ID], tblPublications.[Title/Subject], tblPublications.[Media Tier]
FROM tblPublications;
Save and run the query. See if the correct data from tblPublications was put into the correct fields in the master table.
I ran the Append query as I showed in the SQL above and it inserted the two rows of data for those three fields.
I hope this helps. Let me know if there are still problems.