What are the headphones connected to? They would have to be connected to your phone. For Spotify, the Fitbit only controls your phone Spotify app so the music is still coming from your phone, not from the tracker.
This is different from Pandora and Deezer which allow you to load playlists directly onto your tracker and play from there.
Before posting, re-read to see if it would make sense to someone else not looking at your Fitbit or phone.
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