Why does the voltage of the photodiode "bounce"?
Semiconductor laser effect is described by two coupled partial differential equations of carrier density and photon density, the rate equations.

The solution of these equations result in a non linear current-intensity relationship causing relaxation oscillation when the diode is turned on.

See here or following image:

(image source: p. 45 of this document)  

And what you see is exactly this oscillation near the rising edge of the signal.