Here's a link to a Quicktime showing the renders side-by-side:
The extraneous particles in the Physical Renderer appear briefly in the lower left of that frame. I seem to get a different result each time I render the scene that way (which isn't good, either.)
The guidelines for the Physical Renderer Motion Blur say to bake the dynamics in a scene, but, sadly, you can't bake Thinking Particles. So what does one do?
No extraneous particles are rendered with the Physical Renderer if Motion Blur is deactivated.
I also just found that I get extraneous particles when I use the Standard Renderer and Sub-Frame Motion Blur.
For now I'll make due with the Standard Renderer and Vector Motion Blur, but I'd like to know if this is a bug or if I'm missing a setting somewhere.
Marshall Arts Motion Graphics