Impedance matching photon detector with multiple TTL counting devices
There isn't a need to do anything clever with opamps. Put a Tee piece on your high impedance instruments, daisy chain 50 ohm cables from the source, through the Tees, and finish the daisy chain at the 50 ohm instrument like this (it's a diagram for a 75 ohm system, but the principle's exactly the same)

Note these Tee pieces I refer to are not 'splitters' that contain resistors, but simple Tee connections, zero ohms between all ports and no loading to ground.

This will work whether your source is a low impedance output that will drive valid TTL levels into a 50 ohm load (as I suspect), or a 50 ohm output impedance that will drive TTL levels into a 50 ohm load and >5v levels into an open circuit. I have looked at the data sheet, and it doesn't clarify which, so I suspect the former. If you want, you can tell the difference by running it into a scope with a switchable 50 ohm / high impedance inout and seeing whether the level changes a little, or by a factor of 2.

The way this works is the source launches a TTL level signal edge down the 50ohm line. This is essentially not loaded by each high impedance instrument it passes. Note, fit the Tee pieces to each high Z instrument directly, so the capacitive stub of 50 ohm line is very short and doesn't load the signal significantly. Don't use a Tee to connect 3 bits of cable, and run a cable to the high impedance input, that will get you into trouble! Finally, the edge arrives at the last instrument, and is absorbed in the 50 ohm termination. Each instrument sees one TTL level edge, and one only, and all voltages meet TTL level specs.

There is obviously a progressive time delay down the cable of about 5nS/metre, which has to be allowed for when you analyse your results if that level is significant.