When I go to the app download screen for Hulu, I see the cloud and download icon. I click on it. I'm then taken to another screen saying it's downloading. I select ok. But it has yet to show up in my library.
That is not how the tvOS App Store works on my Apple TV. You would see the cloud-download icon/button with the word Install if the app has been ‘purchased’ before on this device or on another device with the same Apple ID, and is not currently installed on this device. (You would see a Get button with a downward pointing arrow for new apps, unlinked to your account.)
When ‘clicked’, the symbol would change into a rotating loading circle on the same page. When the download is finished, the symbol will change again to the Open icon/button (rectangle with arrow pointing out in the upper right corner).
The apps are all coming from the Apple servers, so installing apps should be the same experience for all apps. Anything app-specific happens after installing the app successfully.
The Hulu app for tvOS has been updated to version 5.37 on 2018-12-03.
The tvOS software has been updated to version 12.1.1 on 2018-12-05.
These are working fine for most users.
If you still can’t get it to install after a cold restart (unplugged for a minute), then ask the Geniuses to assist you.