Here's another thing, from the 2nd PDF...
I finally remembered a search string that found where I had posted this before.
The way I read this is that the low pressure air is that light colored cone behind the axle centerline. The 'Template' line off the top is created by dust carried forward by the tire tread. When it is scoured out by the changing angle of incidence it follows the classic line, it isn't pulled up and forward into the air.
I think this one picture falsifies the pressure normals in the sketch. Probably because of air flows around the sides of the tire as well as over the top. I'd like to see the instrumentation that produced their data.