Automatic Record Numbering in a Shared Database: Not working as expected

I set up automatic record numbering by putting a + sign in the a default value of an integer field, then shared the database. The database already had 6,200 records in the field for which automatic numbering was set up. When I added a record, it assigned 2, then the next one was 3.
So then I used the feature to assign manually the next number, (Database Options/General/Next Record ID#) and set it to 6203, and automatic numbering started working correctly. I conclude that one MUST use the manual number assignment if the shared database has existing numbering in the field to be automatically numbered.

This is correct but is true for any database, whether shared or not.

If I understand you correctly, your database already had numbered records before you turned on automatic record numbering. Panorama doesn’t know anything about these previously numbered records. This is in fact the primary reason why Panorama gives you the ability to manually set the number. When you add the + sign in the default value Panorama will start numbering from 1, no matter what is already in the database. If you want to start with some other value you need to set that manually.

When you share a database, whatever auto-number the single user database was set to is transferred to the server. In your case this number was 1.