I had figured that the detonation was electrically initiated but wondered if the pulse would be fast enough to do that and trigger the camera. They didn’t have diodes but I guess they had capacitors to build delayed signals.
Pretty neat what can be done analog. Many hydraulic circuits have a high degree of programming in them with delays based on pressure pulses as event triggers.
I’m just remembering this off the top of my head, so it might be somewhat inaccurate... Here goes:
One of the trickiest things that they had to develop to make the implosion device was a way to reliably trigger the spherical explosives at the right time and in the right sequence, so that the needed spherical implosion wave had the proper configuration. In the early bombs they had 32 points of detonation to trigger, making this a non-trivial task. They needed to coordinate the triggers within 10 nanoseconds (I think).
Anyway, this was way beyond what was commercially available at the time, so they developed their own triggering mechanism. They did so in the time needed (I think the triggers were only available mere weeks prior to the first test). The method used was an exploding bridgewire detonator, and was one of the most top secret parts of the whole endeavor. The work was done by Luis Alvarez and Lawrence Johnston.
I got most of this from the book by Richard Rhodes. Also, here is a link to a wikipedia article: https://en.wikipedia.org/wiki/Exploding-bridgewire_detonator