I can't explain authoritatively, as I am several years out of this subject and have never been an expert. But I have a few thoughts that may help you uncover a satisfying answer. The NASA report on Project Highwater[1] might also help.

The atmosphere is stratified in steady-state and separated by "pauses" that form boundaries[2]. These pauses are stabilized by various phenomena include gravity, chemistry, inertia, solar warming, radiative cooling, convection. It's all a big fun cesspool of physics that lots of people study. Noting when the test took place, one could imagine a lot of scientific interest motivated by surveillance of space-bound launch vehicles, which were otherwise very difficult to observe. Also, of course, HAMs have a history of observing the ionosphere indirectly with communication[3], think surveillance applications too (not to mention installations like PFRR).

I suspect the phrasing in that Wikipedia article is summarizing a few things that occurred in sequence, eventually resulting in lightning-like phenomena (i.e. rapid electric field equalization over long distances, or noise) on some sensor somewhere:

1. The water launched to that altitude would have still been near STP upon arrival. Relatively speaking, it would have been warmer and released into a lower pressure environment. It's possible the launch could have cooled the water somewhat, but you can only dump so much heat on a short flight! The water was probably packed in some low surface area shape---at least radially circular to conform to the rocket body, and potentially closer to say spherical to aid in stability of flight, to reduce fluid sloth dynamics, make tank strength more manageable with fewer force concentration points, and/or to make the explosion easier to model---so I'm comfortable thinking of it as "hot" water discharged into a "cold" vacuum (around 1e-5 atm at 80km).

2. The water was likely released with some engineered pyrotechnic mechanism that would spread it out as widely as possible and in some tractable shape. I bet a spherical blast would have been the simplest and easiest to achieve, though shaped or staged charges are imaginable, or perhaps they were testing the risk to humans if it were fuel so they had a directional explosion starting from the engine. I didn't do any research down this line.

3. This hot water hits the vacuum with greatly multiplied surface area (from the explosion). The vapor pressure of water would push it into a second stage of evaporative expansion, and it would still also carry most of the momentum of the launch vehicle. I have no idea how to model this, but I am guessing it would be really big and begin to interact with the stratification of the atmosphere and any transport phenomena stabilizing it.

4. The atoms have to go somewhere, at at this altitude they would have had to expand many orders of magnitude. This implies large distances. Also, water is typically not stable at these altitudes, so I'm guessing it decomposed in a way that resulted in the creation of ionized gas.

5. Ionized gas can act as a conductor, and with all kinds of crazy atomspheric stuff happening up there, perhaps it shunted two areas of the atmosphere with significant difference in potential, short of causing visible lightning (see section 5.3 of the report). This would have been resolvable on various instruments and could have resembled lightning on some.

[1]: https://ntrs.nasa.gov/citations/19650011729

[2]: https://www.weather.gov/jetstream/layers

[3]: https://www.hamradiosecrets.com/ionospheric-propagation-of-r...