I'm assuming it's the same with this stain because it has the same warning as oil paints (Which is actually because of the thinners) that you might have to find a waste disposal place?
When I was working with my grandpa's painting company (when it was still a thing) we'd make it a point to always stain the doors inside in the shade for that reason. Bought a little more time for if something came up unexpectedly and you had to leave it for a few minutes.
We also kept the used rags in the center of the room on the bare concrete floor, too. So that even if they flared up anyway somehow, there was nothing around for the fire to spread to.