As I read it, the microwaves did the ionization and the sound waves did the compression. The compression stimulated convection which resulted in the flow patterns they photographed.
Convection in spinning spherical conductive fluids undergoing convection is very complex. There are Coriolis forces, covective forces and magnetic forces to consider. In the Sun, the result is the 22 year solar cycle with many layers of covective cells extending from equator to poles.
Magnetic forces are particularly hard to understand since a conductive fluid moving through a magnetic field generates a current that makes a magnetic field that directly opposes the field that created it.