I describe it slightly differently. Similar to what the author described, I'll first plan and solve the problem in my head, lay out a broad action plan, and then put on music to implement it. But, for me the music serves something akin to clocks in microcontrollers (and even CPUs), it provides a flow that my brain syncs to. I'm not even paying attention to the music itself, but it stops me from getting distracted and focus on the task at hand.