Do I control the unsubscribe handling or do you?

It’s up to you. You can use i-Autoresponder’s unsubscribe handling. You can include our unsubscribe variables: %unsubscribe_url% (for the entire domain) and %tag_unsubscribe_url% (for just emails with this tag) and we will take care of the unsubscribe handling for you. Take a look at your unsubscribe documentation from Control Panel for more information.