Have the version of the Titan Doc that was actually sent via email, be the version that gets saved in Files.

Save in Files the version* of the Titan Doc that was actually sent via email (in Salesforce), instead of the one (template) that is published. 

*I downloaded on my desktop and edited a few values/answers in the document. Then I attached it to the Email that I sent via the Titan button in Salesforce. The email was successfully sent with the edited version. But in Files, the version saved was the template and not the version that was sent.