They will connect to both the watch and the phone at the same time if they are paired. AirPods are the same way....
Audio will play from both by pausing the first one and playing the second. Ex. iPhone is playing audio from a video, if you play a song from the watch it will pause the video and play the song from the watch.
Since the iPhone is better at doing pretty much everything (BT signal, audio streaming and decoding, GPS, etc) the Watch will leverage it the iPhone as much as it can. Also the parent app stores data the Watch is trying to access like the Music app looking for your iPhones library to stream from instead of using Wifi. Many situation will cause it to hand off the task immediately if possible, like phone calls for example.
This is all in an attempt to converse Watch battery life.
The way it works is very seamless, almost impressively so. However it all falls apart if the Watch has a WEAK data connection to the iPhone and/or Wifi. It will still try to gather data but take too long to be of any use, for example
if you were standing just outside of your house.
The spinning dot icon is used for a data connection indicator on the Watch and if you see that its the Watch reaching out for information. Data on the watch reads instantly so if you see that indicator know its looking elsewhere for data and/or additional data.
Knowing that you'll need to start playback with the iPhone close or with it out of range entirely. You can also put the Watch in Airplane mode and turn off wifi (you need to do both) but you're iPhone might be set to mirror this condition making it a pain if you forget to reconnect once your workout is over.
Hope this helps.
