When you install the CMandrill extension we also install the "System - Mandrill" plugin. This plugin is actually used to send the emails through the Mandrill API, so you'll need to enable it once you've provided your API key in the component's settings.
Once you enable the plugin, make sure that everything is working by executing an action on your site that sends an email. The email that you receive then should be coming from mandrill. (look at the sender's name)