I'm guessing, but I think this is worth a try. I suspect that only Public galleries should show up in the Apple TV app.
Your gallery with images for watermarking should be set to unlisted since it is a gallery that should never show to your viewers. Check the gallery visibility (in Gallery Settings... Security & Sharing... Visibility).
The AppleTV app functions just like the rest of SmugMug - if you’re logged in, you can see all of your content.
If you make the gallery Unlisted, you can then logout of the AppleTV app. Go to the “Following” tab and find yourself and mark yourself to be followed. You’ll be able to quickly browse through your photos, but only Public content will be shown.