Simulation by Monte Carlo method of these experiments suggests that those peaks are produced by prompt neutron emission.
[5][6][7][8] This effect of prompt neutron emission does not provide a primary mass and kinetic distribution which is important to study fission dynamics from saddle to scission point.
If a nuclear reactor happened to be prompt critical - even very slightly - the number of neutrons and power output would increase exponentially at a high rate.
The response time of mechanical systems like control rods is far too slow to moderate this kind of power surge.
The control of the power rise would then be left to its intrinsic physical stability factors, like the thermal dilatation of the core, or the increased resonance absorptions of neutrons, that usually tend to decrease the reactor's reactivity when temperature rises; but the reactor would run the risk of being damaged or destroyed by heat.
In that regime, neutron production overall still grows exponentially, but on a time scale that is governed by the delayed neutron production, which is slow enough to be controlled (just as an otherwise unstable bicycle can be balanced because human reflexes are quick enough on the time scale of its instability).