FWIW, in my experiences, CA will NOT on its own initiate combustion. True, it does heat up when mixed with certain other substances but not to the point of ignition. Bear in mind that class A, (ordinary combustibles like wood, paper, cloth, etc.), require temps in the range of 400 degrees F. to ignite. I've used CA on foam rubber material in the past and it "smoked", (fumed visibly like on CSI Miami), and the material "heated" but no where near combustion temperatures.
I don't think you/we have any worries about "accidentally" starting a fire in our shops with CA glue. I haven't done extensive testing on this to verify my summations, but I have noticed that it will react differently with exposure to certain other materials. I found out many years ago when I was doing a lot of plastic modeling and using some photo etched brass pieces, that CA will most definitely accelerate its hardening speed if you blow cigarette smoke on it. It fumes, turns kinda brownish or whitish, gets all "warty" looking, but the end result is the original gorilla glue........ugly as heck but holds like.... a gorilla!
I forgot to offer that those "cotton" cloths were probably a blend with something like polyester, nylon, etc., that reacted with the CA and gave you the jitters. You may want to do a little research if it makes you more comfortable, but in this day of terrorism scares, I feel pretty comfortable that if CA could be used to initiate a fire, govco would have already required background checks and waiting periods just to buy a tube of Super Glue.