You can play Apple Music on Apple TV, but Siri has no clue what’s going on. In the tvOS 9.1 beta, she’s smarter; you can ask Siri to play music from specific artists and Beats 1.
As you can see in the video below, Siri can handle some cursory searches like finding artists or firing up playlists you’ve created. You can also ask Siri to start playing music from specific artists, and start or stop Beats 1.
Even though Apple has this functionality in beta form, it looks decent enough to ship at this point. Unless you get too tricky with Siri — it seems she can’t yet find specific tracks — it seems to work pretty well.
There’s no specific timeline for tvOS 9.1 to ship, so we can’t say when voice control of Apple Music (if Apple indeed includes it in that build) will arrive.