Nuclear explosions are characterized by prompt criticality.
In nuclear engineering, prompt criticality describes a nuclear fission event in which criticality (the threshold for an exponentially growing nuclear fission chain reaction) is achieved with prompt neutrons alone (neutrons that are released immediately in a fission reaction) and does not rely on delayed neutrons (neutrons released in the subsequent decay of fission fragments). As a result, prompt supercriticality causes a much more rapid growth in the rate of energy release than other forms of criticality. Nuclear weapons are based on prompt criticality, while most nuclear reactors rely on delayed neutrons to achieve criticality.
Accidental nuclear explosions are not a new thing.
On January 3, 1961, SL-1 was being prepared for restart after a shutdown of eleven days over the holidays. Maintenance procedures required that Rod 9 be manually withdrawn a few inches to reconnect it to its drive mechanism. At 9:01 pm, this rod was suddenly withdrawn too far, causing SL-1 to go prompt critical instantly. In four milliseconds, the heat generated by the resulting enormous power excursion caused fuel inside the core to melt and to explosively vaporize.
The paper you linked states:
This paper renders the following hypothesis. The first explosion consisted of thermal neutron mediated nuclear explosions in one or rather a few fuel channels, which caused a jet of debris that reached an altitude of some 2500 to 3000 m. The second explosion would then have been the steam explosion most experts believe was the first one.
The first explosion
The idea that Chernobyl involved a prompt criticality at some point was known long before that paper was published. For example, AS Dyatlov, Chernobyl engineer and witness, wrote in his 1991 memoir Chernobyl: How It Was (chapter 1)
At 01:23:47 the reactor was destroyed with an acceleration of power on prompt neutrons. This collapse was the worst possible catastrophe in an energy reactor. No one could comprehend it, no one was prepared for it, no technical measures for localization of the unit and station had been stipulated. Nor were there any organizational measures.
In a magazine article published that year, he makes it clear that this was the first explosion, consistent with your paper.
The main circulating pumps kept up a flow of coolant right up to 01:23:46, when due to a sharp power rise the flow rate through the running down main circulating pumps (loop 1) and then that through the other pumps dropped. The pressure in loop 1 went up. At 01:23:46 or 01:23:47 a large explosion was heard and, one or two seconds later, there was another one, which in my perception was even bigger. And then the silence fell.
IAEA INSAG-7 page 69
Owing to the design characteristics of the reactor, substantial damage to a few fuel assemblies (three or four fuel assemblies are enough) can, and in this case did, lead to the destruction of the reactor itself and the failure of it's emergency protection system. The rupture if the pipes of several fuel channels lead to an increase in pressure in the reactor space and partial detachment of the reactor support plate from the shroud and consequent jamming of the RCPS rods which by that time were only half way down.
Note: The "reactor space" mentioned above refers to the unpressurized space surrounding the fuel channels
That the above was indeed caused by prompt criticality is suggested by analysis results published in the report.
Testimony of reactor operator LF Toptunov
At the moment of the blast (or immediately afterwards) the control rods stopped moving...
From the above, a picture of the first, less dramatic explosion emerges of a localized prompt criticality causing a violent steam leak.
That the prompt criticality and steam leak were both part of the first explosion, rather than two separate explosions, is evidenced by eyewitness accounts and seismic data presented in your paper, both of which suggested a double blast as the first explosion.
The second explosion
This was the more destructive explosion. Ruling out steam, we have two possible mechanisms for the explosion: hydrogen and nuclear.
The core at this point still existed, but the water had already leaked away through the gap between the side walls and the dislodged reactor lid. The very large void effect of reactivity could them allow a second much larger prompt criticality event.
This is supported by the graph below, also taken from the IAEA report.
The threshold for prompt criticality is usually 0.7%, though April 26 1986 at Chernobyl 4 was 0.5%
The first explosion was probably a nuclear blast followed by a steam blast. The second explosion may have been a nuclear blast