If you use "Plex Home" and add your family members to it then they will see content like your wanting.
Further with the newest version of the Android app, if you do not wish to use Plex Home, when a user selects your server from the dropdown they will see On Deck, recently added just like it was their own server.
Is this true for Android on the Big Screen?
I know there is a drop down menu for servers on my smartphone but I haven't seen any option to select a server when using the TV layout on android.
