I have my Spotify account connected to 3 devices. On my main device I have a few playlist saved, but when on the other devices they are not. While I was out my main device (Samsung Galaxy S5) was running low on battery, so I used my work phone (HTC One M7) to listen to Spotify. Unaware that for a period of time, my data was off on the M7, yet it was still able to play songs that were not saved to the device and without any sort of connection. It did not work for every saved songs that were on my primary device, however it still was able to play several songs while not connected. So my question is how do unsaved songs play without any connection. Very convenient feature!
That's a great question and rather odd...is it possible that the music you were playing was saved on the device already elsewhere like in the music library? That's the only way that I can think of. The only way Spotify plays music is if it is using data, the music is saved on the device, or it is saved as an offline song.