Unfortunately, Apple Music (Apple's music streaming service) is not integrated with djay as there is no way for 3rd-party DJ style apps like djay to play songs from Apple Music. This also applies when songs are downloaded onto your device from Apple Music, as the downloaded files will be DRM-protected.
What music can I mix in djay?
Djay provides a sophisticated integration for all tracks downloaded onto your device (via iTunes). You can browse your music library by Playlist, Artist, Album, Genre, Key, History, and more. You can also seamlessly link a variety of outside sources in djay to directly access your own personal music library, such as via Cloud Services, iCloud Drive or external media (e.g., USB drives, etc.), or from other apps on your iOS device.
In addition, djay offers a variety of streaming service integrations with TIDAL, SoundCloud, Beatport, and Beatsource, giving you instant access to millions of tracks and videos. With any of the supported streaming service subscription options, you gain easy access to all of your existing playlists, powerful search capabilities, and Match for intelligent track recommendations.