I think the plasma region has a different kinematic viscosity than the un-ionized region. This should change the Reynolds number (ratio of inertial to viscous forces), and that should profoundly affect things like flow separation, turbulence onset - lots of things that matter in flow over airfoils.

There's been work on kinematic viscosity changes due to plasma effects in plasma torches, but I can't provide links right now.

It will be interesting to see how this holds up in real flight conditions: icing, bug splat debris on electrodes, low pressure at high altitudes, and how much electrical power is needed to sustain the benefits. Cool work.

Strange stuff seems to happen when a neutral gas and a plasma "collide": https://en.wikipedia.org/wiki/Critical_ionization_velocity

One guess could be (as the WP article above seems to imply) that kinetic energy that would normally go into turbulence instead goes into ionizing the neutral gas (i.e. surrounding airflow). That would transfer kinetic (turbulence) energy into electrostatic energy, and thereby of course reduce turbulence.

But this is just a hunch.

Just a guess. Ionized plasma has charges that attract or repulse air particles. Attracting air particles would make them hugging the surface more.