Your understanding is mostly correct. The issue with the fuel rods is that they were double purpose - the lower portion actually increased the reaction rate, w

Your understanding is mostly correct. The issue with the fuel rods is that they were double purpose - the lower portion actually increased the reaction rate, while the upper portion decreased it. Because the team had manually fully retracted the rods, both portions were outside the reactor vessel. When it scrammed, the first portion to enter the vessel was the lower portion, which counterproductively increased the reaction rate further. This was one of several poor design choices in RBMK reactors. You are correct that the people on shift did everything wrong at every step along the way - alongside management, who pushed forward the safety test that caused the accident on a skeleton night shift who hadn't explicitly prepared for it. The test deliberately had the reactor operating in an unusual, low-power state because it was supposed to test whether you could use momentum still in the turbines to bridge a gap until emergency diesel could be brought on line in the event of a power failure affecting the pumps that circulated coolant water to the reactor. However, the shift let the power in the reactor get too low, starving the reaction, and then took increasingly dramatic steps to attempt to bring the power back to specified (low but not that low) levels. These steps included disabling automated control of fuel rods, decreasing the rate of coolant flow, the removal of 18 of the 28 'fail-safe' control rods which were never to be removed, and disabling most of the automated scram mechanisms. Obviously, these steps were not normal procedure and constituted serious flaws in judgement. Normal procedure would be to shut down completely when power levels drop that low, and then a waiting period and a several-hour-long startup procedure. The extremely low power state allowed a phenomenon called xenon poisoning to build up, which made restoring normal operation difficult - hence the normal procedure to shut down completley and allow the xenon to naturally decay. The attempt at restoring power despite this condition led to very unstable neutron flux, and with it unstable core temperatures, triggering alarms from several systems that were continually ignored. Finally, the flaw in the design of a positive void coefficient (meaning that as heat goes up, water turns to steam, and the presence of the steam causes the reaction to become more efficient and produce more heat, in a runaway) actually struck, as the unstable neutron flux presumably spiked and the coolant flow was already further decreased (they had started the actual test, so the coolant pumps were being powered only by leftover momentum in the turbines). In combination, large steam voids formed, and then thermal runaway, and then a scram that actually first increased reaction rates further. (And then fuel rods fractured and many control rods got stuck at only 1/3 insertion, with the increasing portion still within the reactor). The void coefficient is why the test was supposed to take place around 700 MW, not the ~200 the operators had managed to restore; above around 700 MW the void coefficient in RBMK reactors is negative and such a runaway would not occur.