Exit Sub not working properly?

[phoeneous]

This procedure is used to search through a database of customers via first and last names. If the user leaves the txtSearchFirst or txtSearchLast fields empty, a msgbox is displayed and the search is cancelled. Why is the sub continuing to the next lines of code if it should be exiting the sub?

Private Sub cmdSearch_Click()
 
    If txtSearchFirst = "" Or txtSearchLast = "" Then
        MsgBox "Missing information for a valid search", vbCritical, "Warning!"
        Exit Sub
    End If
 
    adoSearch.Recordset.MoveFirst
        
    Do While Not adoSearch.Recordset.EOF
        If adoSearch.Recordset.Fields("First Name").Value = txtSearchFirst And _
            adoSearch.Recordset.Fields("Last Name").Value = txtSearchLast Then
            MsgBox "Match Found!", vbInformation, ""
            fraResults.Visible = True
            imgResultsGirl.Visible = True
            imgWelcomeBack.Visible = True
            lblWelcomeName.Caption = txtResultFirst & " " & txtResultLast
            lblWelcomeName.Visible = True
            txtResultFirst = adoSearch.Recordset.Fields("First Name")
            txtResultLast = adoSearch.Recordset.Fields("Last Name")
            txtResultStreet = adoSearch.Recordset.Fields("Street")
            txtResultCity = adoSearch.Recordset.Fields("City")
            txtResultState = adoSearch.Recordset.Fields("State")
            txtResultZip = adoSearch.Recordset.Fields("ZipCode")
            txtResultPhone = adoSearch.Recordset.Fields("Phone")
            txtResultFax = adoSearch.Recordset.Fields("Fax")
            txtResultEmail = adoSearch.Recordset.Fields("Email")
            adoSearch.Recordset.MoveNext
    Loop
            Else
            MsgBox "No Match Found", vbInformation, ""
            Exit Sub
        End If
            
End Sub