I'm writing this after Spotify Support asked me to do as there might be other people experiencing the same (or similar) problem.
I own a Samsung Galaxy S4 (Android version 5.0.1) and Samsung Gear S3 (Tizen version 184.108.40.206). Spotify is installed on both of my devices. I also use Spotify widget on my Gear S3, for easy access to the app.
The problem is when my watch connects to the phone, Spotify launches immediately on my phone. This also happens when I scroll (or turn the widget wheel?) between widgets on Gear S3, without interacting with the Spotify widget. This is becoming kind of annoying because I have to close Spotify before using my phone. I also need to charge my phone more frequently if I don't realize Spotify is launched on my phone.
Keep in mind that this issue might be specific to Android version 5. After contacting Spotify Support, they asked me to try to recreate the problem on another phone, with an Android version higher than the previous one. I tried it using LG V20 (Android version 6, if I recall correctly now), and there was no problem at that time.