Why does overshooting occur when probe's adjustable capacitor is under-value
It isn't the rise time or fall time of the signal edges that has the exponential effect; it happens once the probe has let the edge through - that's when the RC time constant takes place.
If your scope probe is over-compensating for the scope input capacitance, the ratio of probe capacitor to scope input capacitance might be 1.1 higher than the resistive divider gain so inevitably you would get the &quot;edge&quot; of a transient being passed through with a &quot;gain&quot; of 1.1 however, once the &quot;edge&quot; has finished, the resistive part of the divider erodes the &quot;gain&quot; of 1.1 back down to 1 and that is where the exponential decay takes place.
A typical probe capacitor setup

Image source.
I'm talking about the capacitor referred to above as &quot;LF Compensation Adjustment&quot; i.e. that capacitor is 1.1x higher than for the required compensation.
Idealized capacitive voltage divider
So, if you were to have a scope that used a purely capacitive voltage divider (with a &quot;gain&quot; of 1.1&quot;), the waveform would be more like these additions in yellow: -