Welcome at the Spotify Community!
You can only use Spotify on one device at a time. Let's say you have 2 devices with the same account, A and B both want to listen to music.. that won't work. Only A or only B can listen to music, but not at the same time.
Also you say you start it at A and you hear it on B.. do you have Spotify Connect enabled? If yes, please make sure Spotify connect is off.