For the life of me I can't remember what the distance between
boosters is supposed to be, but you're essentially right. The
actual explosive charge is detonated by a shock wave and not heat.
The shock wave is provided by the PETN in the det cord as it
detonates, but as it burns along, more force is directed outward
than along the length of the cord. As such, the shock wave
diminishes along the length of the cord, and the detonation of the
boosters is used to increase the shock wave, a top-up, as it
were.