All the documentation and guides I've seen point to using Mandrill directly, instead of through Heroku.
How do I add an inbound e-mail address & webhook?
I think you need to look at Mandrill documentation on processing inbound emails.
From this, it looks like there is nothing special about doing this in Heroku - as long as you have a web page in your site to handle the inbound message, all the configuration is done with the Mandrill dashboard.
Have you checked out the documentation on using the Mandrill add-on with Heroku? It's available here with examples for multiple languages:
https://devcenter.heroku.com/articles/mandrill
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