It can be tricky to make edits to the results page. The columns and table info that you see when you edit the DataAssist Search server behavior come from the recordset that the search is applied to.
In order to get your updated table info available in the server behavior you would first need to edit the recordset on the page to add in your table or columns. If you have just added a column to the existing table that is being queried you should be able to just add it this column directly to the sql.
The recordsets on this page are very advanced and would require advanced sql knowledge to edit. These recordsets can be difficult to edit correctly.