Fisheye lens calibration
It seems I found an answer on the Panotools Wiki:


  Unlike rectilinear lenses, fish-eye lenses do not follow the
  tangent-plane geometry, but instead have built-in distortions designed
  to achieve wide fields of view. The radial lens distortion parameters
  are used the same way for rectilinear lenses and fisheye lenses, but
  they should never be used to attempt to remap a fisheye to a
  rectilinear image. This is done by selecting the proper source and
  destination projection. Fisheye geometry follows a rapidly-changing
  trigonometric function which can hardly be approximated by a third
  degree polynomial.
  
  For fisheyes, the lens correction parameters correct for the deviation
  between a real lens and the ideal fisheye geometry.


The last sentence suggests that the lens correction is done to get a proper geometry of whatever lens it is. The fisheye is therefore remapped after the lens corrections are done.

Looking at the Fulla tool source code from Hugin, it seems that it performs corrections in the following order:


Flat-field correction (i.e. removing vignetting
Radial distortion correction (barrel, pincushion, wavy distortion)
TCA correction (i.e. removing one type of chromatic aberration)