Difficulties supplying 5V TTLs to 50 Ohm terminated single photon counter
The NI box specs for Ioh are either 16 or 24 mA.

1 volt into a 50 ohm load requires 1/50, or 20 mA.

2 volts into a 50 ohm load requires 2/50 or 40 mA.

So you would expect your NI box to produce pulses on the order of 1.5 volts, since in general you'll get better than minimum output.

And this is exactly what you are getting.

Using standard TTL to drive 50 ohms is a problem which goes way back. I'd advise making a little box to go between the NI and TCSPC which uses a MOSFET driver and run it off 5 volts. Something like a MAX4426/4427. Connect the NI box to your buffer box directly (no coax, or as short as humanly possible - preferably make your buffer box with a female BNC connector on the input), and put about a 200 - 300 ohm resistor on the buffer input as a partial termination. If you don't like the results from a MOSFET driver, use a 74FCT244 with all 8 inputs tied together and all 8 outputs tied together. Use only a P output from the NI box.