Yep it works for me too. My phone streams to my watch and my pods paired to my watch so i could use the crown instantly
I don't think that is the case. The phone is streaming to the headphones but the "Now Playing" app on the watch will allow you to control the volume as well as pause and skip tracks on music playing from the iPhone. Thats how it worked with my Senhieser Bluetooth headphones and I suspect it works the same way with the AirPods.