Extrapolating parameters for SPICE model for a Silicon Photomultiplier
I don't understand these types of sensors but I have worked on similar sensors and spice models. The best I can tell you is match up the waveform in the datasheet with the one in the model. Sometimes you have to match models up by trial and error, sometimes all the parameters are there. A lot of the parameters in this paper are on the datasheet, get some smarts and find them. I don't have a lot of time for this question but I'll give you a head start. You need to math these figures up, your spice model should look like the "Standard Output Pulse Shape"

Secondly: The overvoltage is given in the model as \$V_{ov}= V_k-V_{BD}\$, in the datasheet its listed as \$V_{br} +2.5\$ (as an example, its model dependent) and \$V_{br}\$ is nominally 24.5V.

It sounds like you need to spend some time reading the paper, but this should give you a good start.