A question about effect of external trigger to the risetime a driver output

A laser driver outputs very short pulses with very fast rise times required for some laser diode applications. But the driver requires an external trigger to operate. I want to give an example scenario to make my question clear, and expecting an estimate approximate answer.

Here is the manual pdf.

The manual states that the driver output's rise/fall times as 100ps.

My confusion is, will the external trigger source I will use affect the driver's output rise time or it will only affect the jitter?

Figure 1 in that manual, it looks like a Schmitt trigger on the trigger input (0.5 V). The manual says the device can provide 250 picosecond pulse width.

But I need an external trigger source for this device. And if I use a microcontroller PWM the rising edge of my external trigger can be up to 100ns. If by using an external trigger device I provide 1MHz pulse train with 100ns rise time(fx. from a microcontroller) to this driver, will the driver output's rise/fall time affected? Basically I'm asking whether my external trigger rise time will affect the device output's rise-time.

(I hope my question is clear enough and I'm satisfied with some approximate answer since I cannot provide more details at the moment.)