Syncing across iOS devices and OS X

[artlevit]

This seems obvious-but I'm new here: if I create a playlist on my iPad, doesn't it sync to my other devices with Spotify (iMac and iPhone)--at least when there's wi-fi around, or via cell signal? I spent a lot of time adding songs to a playlist on the iPad but it hasn't shown up on iPhone or iMac. Yet, a playlist I created earlier on the iMac did download to the iOS devices.