Not sure this is Cortana related, my 1520 has done it since before Cortana was on my phone.
I can't recall if it started with first developer preview or if it happened a couple of times before but I know Cortana was not on phone when I found this issue.
Listening to music and I get a notification then at random times the music starts to come out of the speakers and the earphones I need to stop the music, unplug the headphones, plug back in and press play for the issue to be fixed.
Very annoying in the office sometimes.