There was some synergistic effect that suddenly caused that area, when they dropped the rods in, to exponentially increase power. Power was doubling every second. Not a linear increase. That’s documented.
It may actually be coincidental that it exponentially increased in power then exploded after they pressed the AZ-5 panic button to shut down the reactor by dropping the rods.
However, their nuclear physicists came to the conclusion that the design flaw was the tipping of the control rods with graphite that was the proximal cause, along with the design being notoriously touchy to control at low power levels, being designed to run at higher power. The two lower lever, line engineers, had done everything according to protocol, including pressing AZ-5 to abort the test. The senior engineer had over-ruled their objections, spoken several times prior to starting the test, that he was breaking the protocols for the test by performing it at 200 MW rather than at the protocol 700 MW to 1000 MW as they had been instructed to perform it, once even demanding he put his orders in writing in the log. Neither of the younger engineers survived radiation sickness beyond a few weeks of the event. Ironically, the senior engineer who broke protocol lived until 1995, dying of a heart attack.
The Chernobyl plant had been rushed to completion as well, with specs fudged by on site Party member managers (the roof, for example, was designed to have been built out of non-flammable materials, but to meet a bonus goal for the plant manager, it was constructed from wood instead), that night’s test was to have been done before reactor #4 was commissioned, but instead was done after the reactor was put on line, again to meet a bonus date for the plant manager.
What’s currently worrisome is that the entire exclusion zone around Chernobyl has been systematically stripped of metal by looters with the complicity of corrupt military members of Russia and then later by military forces of Ukraine since the fall of the USSR. This metal has concentrated radiation, some of which has as high as 30-50 mSv/hr or perhaps even higher of induced radioactivity. 1 mSv/hr is considered dangerous exposure. There were thousands of military vehicles abandoned in the containment zone after the cleanup, bulldozers, tractors, etc. These looters, none wearing protection, are smuggling this metal out of the containment zone to sell to recyclers who in turn sell it to smelters in Russia, Ukraine, and China and elsewhere and the radioactive metal has been detected in products around the world. Some of the buildings in the area have been stripped entirely of their metal. It’s estimated that almost 800 tons a day are being smuggled out by these looters through the military guarded gates into the area.
The area around the disaster area is so radioactive that construction workers who are building the new moving “Sarcophagus” to contain the radioactive plant which when completed will be moved to cover over the plant, are allowed to work only ONE eight hour shift per month. . .
Sure, and we know why. Running at 200 MW got them into what is known variously as Iodine Valley or the Iodine Well or Xenon Poisoning. Within the fuel rods this stuff normally burns off in the neutron flux in normal operation. At low power levels, though, it builds up. Both Iodine 135 and Xenon 135 will decay by themselves in time (half lives of 8 and 12 hours respectively IIRC, although I didn't look that up). But while they're still there both have large neutron capture cross-sections and soak up the neutrons that would normally be moving between the fuel rods. And bringing a reactor in that situation up again by pulling the control rods means that nothing happens for a while, which tempted them to bring them up still further, and so they did. The exponential increase in power was essentially a reflection of the iodine and xenon burning off within the fuel rods, and when it finally did so the reactor was running wide open. It gets hot faster than humans can react and faster than the control rods can descend. They did get the rods moving, but as you say, it made things worse.
This was compounded by the lack of real-time measurement. The actual heat distribution within the reactor was only visible after the equivalent of a 286 computer crunched the input numbers and printed the profile out on a dot-matrix printer. That process meant that the operators were always 10 minutes behind what was actually happening. Minutes for a decision, seconds to move the rods, heat increase in milliseconds. "Unstable" is an understatement.
My sources for this, if anyone cares, are James Mahaffey's Atomic Accidents and Grigori Medvedev's Truth About Chernobyl, (formerly "Chernobyl Notebook"). Great reads, both of them. Medvedev was the guy who was flown in to clean up the mess.