Some poor marketing decisions at Apple make it difficult to tell the difference between the "Apple Music" streaming service and the Apple "Music" app which can play music on your phone as well as streamed music from "Apple Music".
Try specifying "in my library" if you're asking Siri to play music you have stored on your iPhone. If you're trying to stream from the "Apple Music" service (via Apple's Music app), check in Settings to make sure you have enabled Cellular Data, and that you have joined/enabled that service.