Hi MeganFang1101,
While not able to speak to the app or service you mentioned, there are ways to listen to Apple Music via your Apple Watch without the paired iPhone nearby.
From the support article Play music on Apple Watch:
"You can play music stored on Apple Watch, control music on your iPhone, and stream music from Apple Music and Apple Music Voice if you’re a subscriber."
and
"After you connect Apple Watch to Bluetooth headphones or speakers, open the Music app
on your Apple Watch, then do any of the following:..
- Play music from your music library: Tap Library, then tap a playlist, artist, album, or song. To play music downloaded to your Apple Watch, tap Downloaded, then choose music."
Further confirmation is outlined in Add music to Apple Watch:
"Add music to Apple Watch
When you add music to your Apple Watch, you can listen to it wherever you go, even when you don’t have your iPhone with you.
You can add specific playlists and albums to your Apple Watch using the Apple Watch app on your iPhone. If you’re an Apple Music subscriber, you can also add music with the Music app
directly on your Apple Watch."
Regards.