It would be a long explanation, but here are a few key things happening at supersonic to hypersonic Mach numbers. I'd add "approximate" in front of each of these statements as there are a lot of additional details going on.
1) Subsonic the fin center of pressure is approximately at the 1/4 chord point, supersonic it is approximately at the 1/2 chord point. So initially the rocket center of pressure moves aft as the rocket goes through Mach 1.
2) As the Mach number increases, the CNalpha of the nose cone increases and the nose cone CP moves aft towards the nose cone/bodytube junction. Eventually the nose cone CNalpha decreases and the nose cone CP moves forward, both back towards their subsonic values. Eventually at hypersonic Mach numbers, based on linear theory, the nose cone CNalpha and CP return to close to their subsonic values. The increase in the nose cone CNalpha at supersonic Mach numbers up to Mach 3-4 moves the rocket CP forward.
3) At supersonic Mach numbers, once the fin leading edge goes supersonic, the fins constantly lose lift. Based on linearized theory for a thin airfoil of arbitrary shape, planform (delta, swept) independent, the lift coefficient, shown as a small cl here, is determined from the equation below. At small angles of attack normal force coefficient is approximately equal to lift coefficient, so take the derivative of the equation with respect to angle of attack, and you get CNalpha. Note that as the Mach number increases, the CNalpha of the fins is decreasing via the one over square root of Mach number squared minus 1 term. This is a major contributor to the rocket CP moving forward at supersonic Mach numbers. (Once it has done its initial move aft due to the 1/4 chord to 1/2 cord fin CP shift.) Note wing sweep (not included in this equation) has an important effect here, the max supersonic CNalpha of the fin occurs when the fin leading edge goes supersonic, and then decreases past that point.
Again, put "approximate" in front of the above statements, and there are many more additional details, fin leading edge sweep being a big one, and fin planform shape (delta, swept, tip chord to root chord ratio, etc.) having other important effects.
Chuck Rogers
Rogers Aeroscience