Why did "tickling the dragons tail" by Louis Slotin not cause an explosion? I have been reading the excellent Command and Control by Eric Schlosser and discovered more about Louis Slotin's experiment with "tickling the dragons tail" and the infamous Demon Core.
What I don't understand; and please excuse my naivety, is when the accident on May 21st, 1946 occurred and Slotin's screwdriver slipped causing the reflector to close around the core and the core becoming supercritical:

On the day of the accident, Slotin's screwdriver slipped outward a fraction of an inch while lowering the top reflector, allowing the reflector to fall into place around the core. Instantly there was a flash of blue light and a wave of heat across Slotin's skin; the core had become supercritical, releasing a massive burst of neutron radiation estimated to have lasted about a half second.[10] He quickly flipped the top shell to the floor. The heating of the core and shells stopped the criticality within seconds of its initiation,[11] but Slotin's reaction prevented a recurrence and ended the accident. Slotin's body's positioning over the apparatus also shielded the others from much of the neutron radiation. He received a lethal dose of 1000 rads neutron/114 rads gamma[5] in under a second and died nine days later from acute radiation poisoning.

Why did the core not explode/react? My understanding is that the core 'is' the bomb and once the chain reaction begins and occurs in trillionth's of a second could not possibly be stopped in time by the reactions of Slotin alone?
I have tried to source information to fill my knowledge gap, but am perhaps using the wrong terminology to ask the question. Can anyone assist? 
Finally, and once again, please excuse the naivety of my question.
 A: Your understanding is pretty much correct and your question quite a natural one. 
The core did react: the release of energy heated the core and shells quickly, thus changing the neutron capture cross section for the plutonium in the core. A plutonium (or any fissionable) atom's ability to capture a neutron and undergo fission is weakly dependent on temperature: decreasing with increasing temperature. As the core heated, the lowered ability to capture neutrons meant that the core actually became subcritical pretty quickly, thus quenching the chain reaction. If Slotin would not have flipped the top shell off, the uncritical core would then begin to cool and become critical again, repeating the process.
Generally, and thankfully, big bangs are very hard to provoke with nuclear chain reactions. The immense release of energy in a small space means that the critical mass is going to heat up and quench the reaction very quickly. If you do get to explosion, the mass blows itself apart, quenching the reaction even more quickly, so unless there is very particular conditions, the bang is not going to be a big one: just enough to break apart the apparatus and drench every living thing nearby in a lethal dose of neutrons. Big nuclear explosions only happen when the process of assembling the critical mass is so fast and the process of crushing the critical mass and keeping it confined does so long enough that a huge amount of material has time to undergo fission before the core blows itself apart and puts an end to the whole process. In a plutonium bomb, this is done by crushing the hollow core with shaped explosives that produce a highly symmetrical, inward moving shock wave. 
A: I can only answer qualitatively:
The experiment where the death occurred was on a subcritical mass of plutonium, and reflectors were being used to bring the number of neutrons to the ones required for criticallity.

The mean generation time, Λ, is the average time from a neutron emission to a capture that results in fission


and l is the the prompt neutron lifetime , the average time between the emission of neutrons and either their absorption in the system or their escape from the system

k = 1 (criticality): Every fission causes an average of one more fission, leading to a fission (and power) level that is constant. Nuclear power plants operate with k = 1 unless the power level is being increased or decreased.

k less then one is subcritical, and k larger than 1 is supercritical, the explosion stage of weapons.
They were experimenting on turning a subcritical lump to critical by using reflectors and increasing the number of neutrons in the sample.
Times in these experiments from subcritical to critical depend a lot on the boundary conditions, and in a sense the accident is an experiment. It tells us that subcritical can go to critical within times controllable by humans , i.e. seconds, ( though they do not survive). His reactions were fast enough to stop the chain reaction, though it is not clear whether the lump of plutonium would have gone to supercritical if the reflectors were not removed.  The subsequent to the accidents precautions of using remote control and the observes at miles distances shows that the danger existed.
Anyway the experiment tells us that even though the prompt neutron lifetime is in microseconds the build up of the chain reaction for this particular geometry and mass is of the order of seconds, enough for a human to react.
A: For a nuclear explosion you must create a super prompt critical configuration and maintain the configuration for many neutron generation lifetimes, while pressure is attempting to dis-assemble the material into a non-critical configuration. Manual assembly cannot maintain the configuration sufficiently long for a nuclear explosion to occur; it can cause a brief nuclear excursion releasing a significant amount of radiation.
(A certain fraction of the neutrons from fission are delayed as they result from decay of fission products, as opposed to prompt neutrons released at the time of fission. Prompt critical means critical on the prompt neutrons alone without requiring the delayed neutrons to be critical.  You may find my answer at Why does nuclear fuel not form a critical mass in the course of a meltdown? interesting)
