I would assume that the table where you are reassigning the salesman is keyed with its own primary key, and this is what should be selected in the multi-select list box.
Your SQL string is selecting all the records for a particular salesman to be updated to the value in the AssignTo combo.
I created a small test db with a salesman table whose primary key is used to indicate the assigned salesperson in the FollowUp table. The listbox has its source set to a select query with a criteria of "SalesmanID = [cboFrom]" and the bound column is the primary key of the FollowUp table.
Your strSQL should have a criterion section of "WHERE FollowUpID = " & lstDisplay.ItemData(intCount)