Handing off between devices is my current pain point with it. It can group players so that you can do multi-room synced play, but I use that to hand off from my desktop to my phone. You can transfer the active playlist to another device. But in either case it's a manual interaction and doesn't "just happen". To be fair, I didn't have 100% success rate with Spotify doing this correctly either. Sometimes it did it, sometimes it just started in its own world.
The MA IOS app is REALLY rough; but I have had very good success with Xonara on ios, which is currently available through testflight.