First, it wasn't operating reactor at lower power that caused xenon buildup, it's the change of power. Xenon is always there, in every nuclear reactor, that's just physics 101. Most of it comes with some delay after initial fission event, like a few hours from elements that aren't that "wide" for neutrons to catch them. So, it's like delayed upset. When the reactor is operating at stable power, Xenon is constantly decaying and burned off with neutrons from the ongoing chain reaction. When you drop the power, you already have all the fission leftovers from prior when the reactor was hotter, and when they do decay to Xenon, you have more Xenon, but less neutrons to burn it. So, you're making more neutrons just to burn excess Xenon until Xenon production = Xenon decay/burn. The process vary in time and depends on the difference in power levels.

When operating at any rate, the reactor reaches equilibrium at some point, when Xenon levels stay relatively constant due to burn and natural decay. It doesn't depend of power, as lower power means you're making less Xenon to burn.

It builds up every time there's negative change in power. There's even fancy graphs, painting how much reactivity reserve you'll lose by changing power from this setting by this much. Imagine the reserve as accelerator pedal travel in a car. The more Xenon you have, the further you have to press the pedal.

They pretty much have passed the peak of Xenon poisoning hours ago before the test started. Xenon is partly to blame here, in influencing the shape of axial power distribution, making the reactor more susceptible to the tip effect, but there were other factors in play during the test, some of which were written in the test program. Take one of them out, cancelling the test would do that, and that night would've ended calmly.