Does the Hydrogen/Chlorine reaction in light proceed instantaneously?
It depends on how much UV is used, and how it's distributed... from a point source, the flame front would spread as if from an automotive spark plug. In fact, lasers are being tested as a means of ignition in Otto-cycle engines because the flame front can be better controlled than from a spark.

If evenly spread over the surface, as in laser fusion attempts, then the wave-front would propagate from the exterior inwards. Theoretically, using fiber optics inside the container to distribute and delay the beam equally, the explosion could propagate as fast as desired, with the caveat that the delay would still be half the largest space between tips.

This means, for example, that a one-cubic-meter container could be made to explode in far less than 1/3*108 seconds, which would be the minimum if it were to be ignited at the edge. Though not truly simultaneous throughout the container, one can approach any finite speed, even, apparently, greater than light. This is similar to other phenomena that exceed C, such as the crossing point of scissors or the phase velocity of a wave.