WP Users Media is a WordPress plugin that displays only the current users media files and attachments in WP Admin.
WP Users Media works right away when you activate the plugin. No more settings needed.
If you need the options switched on for the Admin also you can do it in the Options Page located in the Settings area.
What the plugin does is to disable the ability for users to access other members files and attachments through the Media Button and Featured Image sections. This is really good because maybe you have Authors, Contributors and Subscribers that writes posts etc. and you do not want them to be able to use other members media files to their own content.
To test it out create
1 Admin and
2 Author's for an example. As Admin you are able to see all media files from all the users on the site.
Author 1. Log out.
Author 2. As you can see Author 2 cannot see the files uploaded from the Admin and from the Author 1.
This is very effective solution to keep the media files more private.