not necessarily. You might pick a frequency, and just have an amplitude detector, as suggested above. When you push the button, the frequency starts to oscillate, and a few nanoseconds later the signal is detected. No modulation or coding needed. ADL5506 log detector will have a good dynamic range, AND only take 100 ns to turn on. But if you have to add a bandpass filter in front of it, the latency wil increase as the inverse of the bandpass filter's bandwidth
If you are in a congested area, you might make two receivers, one tuned to say 433 MHz, and the second tuned to 2450 MHz...and you only flash when BOTH of them get turned on
A more complicated way would be to set up a comunications link with modulation, with a high bit rate...say 500 MBPS, and send a short code to fire. That would be much more battery draw intensive though