Basta adicionar uma chamada a CallOtherProgram
em seu procedimento original:
Public Sub SaveAttachmentsToDisk(MItem As Outlook.MailItem)
Dim oAttachment As Outlook.Attachment
Dim sSaveFolder As String
sSaveFolder = "C:\Users\username\Documents\"
For Each oAttachment In MItem.Attachments
oAttachment.SaveAsFile sSaveFolder & oAttachment.DisplayName
Next
CallOtherProgram
End Sub