Spotify Connect is a feature that allows you to switch between the devices your Spotify account is logged into. It will have a popup asking if you want to switch devices when you open Spotify on one device while already listening to Spotify on another device.
Is this change in playlist only happening after the popup asking if you want to switch devices shows? If it's happening other times, too, you might have a stacked queue problem. To check this, click the queue button at the bottom right of the now playing screen. If you have a stacked queue from a playlist you are not currently listening to, they will show in "Next in Queue."