Show layout.
What they are plotting is the waveform used to measure surge capability. I don't know that anyone actually specifies response time, in terms of having a fixture to actually measure it; I think it's just assumed. Rest assured, avalanche breakdown is very fast -- the limiting factor in circuit, is the path to the diode, not the diode itself. In particular, at these impedances, stray inductance.
So, it's very likely that layout is to blame for the lumpy waveforms.
Tim