I've noticed via browser on Adobe CC forums site that my activity feed showed that I made a pattern and a shape "public".
Where are they?
How do I see others' works that are public?
What can you do with public assets?
What are the copyright implications of using them in your own work?
How do you make them private again?
In order to make your own Color Themes private before saving them make sure to tap on Private on the Info screen. If they're already set to Publish, you can go in and change them in the app. Just tap on the Color Theme you'd like to make Private. Tap on the Info tab. Then Edit (in the upper right corner). You'll be able to change the setting in the Edit Info menu. Just make sure to Save your changes.
Since there is no public venue for them, Brushes, Shapes, Looks, and Patterns have the setting Create Public Link and anyone with that link will be able to see the asset on Adobe Creative Cloud. But, unless you give out the link, no one would have it. However, you can also save/edit those assets in Capture CC the same way as Color Themes.
I hope I've understood your question correctly. Let me know if I haven't or if you have any questions.