This is one of the general problems about PaaS. One of the tenets of 12 factor is that "12 factor processes are stateless and share nothing. Any data that needs to persist must be stored in a stateful backing service, typically a database"[1] which is why we want to avoid persisting state in the container.
Content Management Systems like Drupal or Wordpress typically store file uploads or configuration files directly onto the filesystem. With Deis or any other PaaS, this filesystem is ephemeral unless there is a shared filesystem mounted inside the container, typically via SSHFS[2] or some other remote filesystem.
We want to tackle this problem with a service gateway[3] for apps to attach backing services like a shared filesystem, but for the moment there's always S3 :)
[1]: http://12factor.net/processes