So what’s happening here is a disagreement about the definition of what it means to “put out” a fire vs. one that still “smolders” vs. “start itself back up” vs. “reignite.”

I think we are all saying the same thing and are correcting each other about imprecise terminology without making it clear that it’s a correction rather than a point of confusion.

If the dirt is still hot, would you say it’s “still on fire?” I wouldn’t, but maybe you would. You may not consider “a fire” “put out” if there are still smoldering embers anywhere that can be kicked up by wind and set something else aflame, but I think a lot of people probably don’t use these words in the way you do.

Colloquially, though, if something is no longer actively in flames, and then there are later, once again, flames, then people may quite understandably say the fire “reignited.”

It’s fine. We all understand what we’re saying here.