I have several forwarders set up and working. I was surprised to find that the messages that were forwarded appear in both inboxes, not just in the destination inbox. Is that the correct behavior? Am I missing some option I can set up or a different way of accomplishing my goal which would be for the message to only end up in the destination only?
That is expected. If the email account exists in “Email Accounts” then it stores. If it exists in “Forwarders” then it forwards. If it exists in both places, it stores and forwards. Reverse either of those variables and the relative result will also go with it.
And the light bulb flashes 
Thanks