Not sharing with those on home network?

You can put media anywhere: it doesn’t need to be in the ‘Shared Media’ folders in the Public share. You can create private shares, and store private media in there, accessible only to those who are allowed access via their MyCloud account and password.

If you’re accessing via DLNA, then you can turn off media serving for your private share. If you enable media serving on a private share, it will be visible to anyone on your local network, because DLNA does not respect access control; that’s a feature of DLNA. Non-served media can be accessed via the file server, rather than the media server. This allows you to access them with a utility such as Kodi, which is a media player that can access the SMB file server on the MyCloud.

Use and control of the Twonky DLNA media server is described in the User Manual, and, in more detail in this FAQ: