I think I understand roughly why point lights are "blown up" into these blur kernels, but why are they perfectly circular with well-defined edges instead of being blurrier further away from the center?
To me it looks like the blur kernels take on a circular shape as expected due to the rays overshooting the focal point, but they don't appear to be perfectly circular to me. For example the circle at the top and bottom of the left side of the image do blur as they expand from the center. The bottom circle seems a bit more perfectly circular but there's still a smudging of light around the edges, and the circles themselves are more warped and oval-shaped.
I think the reason why they might be warped is because the lights aren't always point shaped in reality! The exact circle effect is only for point lights.
Mathematically speaking, a point light is a Dirac Delta function. The convolution of the Delta function with a kernel function will return the kernel function, centered at the location of the point light.