Airpods disconnect with Apple watch

If I listen to music on Spotify on my watch and airpods, do I need to turn off bluetooth on my iphone or the airpods will connect to my watch automatically? And if the airpods can not connect to the watch automatically, does it mean there is something wrong with my watch?

It seems like Spotify on my watch can not work smoothly if I don’t turn off Bluetooth and disconnect the airpods from my phone (Ex. the songs keep playing on the watch but I can not hear anything, I can not skip/go back to the previous song...)