With Spotify open, navigate to Spotify > Preferences.
Scroll down and click the Show Advanced Settings button.
Under the Startup and Window Behaviour heading, change the Open Spotify automatically after you log into the computer dropdown to No.
You're all done!
For a limited time, Spotify is giving away a free Google Home Mini to every Spotify Premium member! So if you pay for Spotify, this guide will show you how to claim your free Google Home Mini.