I'd be worried about if there's ash from the burn off that then mixes with water to become lye. Not sure if there's more of a chemical reaction necessary than that.
I had a vinyl wrap on part of my car and some ash from California brushfires fell on it, and then it rained a month or so after (I was procrastinating on properly washing it off) and the lye produced ate through the clear coat of the vinyl.
Maybe it picks up dirt particles from the air. In my experience, stuff that gets rained on can sometimes acquire dirt that it wouldn't otherwise have. If ky clothes are drenched from the rain, I throw them in the laundry instead of considering them clean.
No doubt, but presumably those non water things are all things that evaporate, so wouldn't get left behind then the rain dries. The rain would have to pick up something up on the way down for it to contain something that precipitates out. That could be dust or soot, I'm not sure what else, but any minerals would have to come in that way
The fact that I'm referring to them as "weird" means that they are not, in fact, normal. Presumably if any of these people had seen such a thing before, they wouldn't be so concerned about it.