It would be awesome if you could help us fix this bug! You can submit an issue here. Make sure to include your device, OS and version and Spotify version so the team can figure out the problem.
In the meantime, a workaround that I have found is to close the Spotify window before turning off your computer. Make sure that it is closed in your taskbar as well as Spotify can stay hidden in the hidden icons section (to be extra sure, I would check Task Manager as well.)