Your watch is not playing music on your phone.
There are a few scenarios that can cause "unexpected" music experience issues but it does depends on your specific situation. If you can provide some details it would probably help.
In a nutshell, if you're using AirPods, then they will by default connect back to your phone if you're wearing them and if the phone needs to provide audible feedback or audio. In the AirPods setting on the phone you can change that setting (Settings, Bluetooth, Airpods)
Then for your music client it will also default to your phone if it's available. So if you're using Spotify and you begin a Spotify session from your watch but your phone has the Spotify app open it may move it back there. There are various ways around that but the easiest ones are:
* Close Spotify on the phone. This will likely solve the issue, but in addition you can:
* Disable BT on the phone (from Settings, not from the Control Centre)
* Disable the AirPod default to phone as I mentioned above.
If you can provide some details on the exact behaviour we can try to help more.