My apologies, I should have been more specific. The plugin for mailgun seems to append the registered mailgun custom domain to every outgoing email. This domain is fully connfigured and operational with mailgun outside of the plugin. For example
Send to firstname.lastname@example.org in Mailgun testing screen. The request received by mailgun API is for email@example.com@mailguncustomdomain.com which of course failed and is dropped.
Mails to addresses on the @mailguncustomdomain.com work.
Hope this helps you