A while back I was changing out a tip on a CA bottle and knocked the capless bottle off and behind my lathe into about 6 or 8 inches of wood and acrylic shavings, worn out pieces of viva paper towels and sandpaper, and probably some other stuffs that would easily catch fire.
It spilled about an ounce of CA and it made a hell of a lot of white smoke and ran me out of that corner of the shop for a few minutes, but after inspecting the big mass of crap that resulted there was no sign of anything having gotten hot enough to actually light up.
And as mentioned, any oily rags should get treated a lot differently. Anytime I'm dealing with oil finishes of any kind I put my applicators/rags into an old tin coffee can until I'm finished doing whatever I'm doing, then dispose of them into my burn barrel immediately after my turning session is done. Back when I lived in town and couldn't have a burn barrel I just put everything outside to dry out completely before disposing in the normal garbage stuffs.