Yeah, it's a bit unclear.
It makes a bit more sense if you research the actual meaning of the story. The point of the tale was that the curse the village chief suffered is just the result of the strong feelings he felt at seeing the kids kill the snakes. The kids didn't give a shit, and so nothing happened to them. (As with many such stories, there's an entirely prosaic explanation that this "curse" is just the chief being traumatised...)
So this explains where the snake came from during Mizuki's run down the road. The specific creature here at the start of the chapter (the Jatai) doesn't actually appear, because Tomoe isn't that much of a jerk-ass, but instead it's Mizuki's fear manifesting itself. In this story Mizuki's decision to involve herself, and Shizuru's decision to warn Mizuki about the dangers, ironically made things worse for them than if they did nothing and just let the scarf get burnt. So if they were like the kids in the story they'd have been better off, but they can't.
This isn't spelled out unfortunately. Maybe it's clearer in the anime?