The 11.5-16VDC seems to be when plugging it into e.g. a car's power jack (cigarette lighter), sometimes also found on airplanes (first class, maybe, though I think those are all standard outlets now as it is), and has nothing to do with output voltage.
It likely is 19V output as stated on the back (manufacturer probably knows better than the people who wrote the documentation/packaging/promo fluff) and at some retailers (e.g. maplin) who didn't just copy/paste the material, and that would explain the fan going faster than it's supposed to if that's pretty much just hooked up (semi)directly.
The jalapeno's mining portion itself is behind a bunch of voltage regulators, so that should be okay. Those voltage regualtors themselves may run hotter than they're supposed to, though. They may well be able to take it, but why take the risk?
Find a proper 12V brick. You can find plenty for cheap with plenty of oomph: 12V 5A, 12V 6A is fairly common as LCD monitors use those a lot. You can't use those as a travel power supply, but if you're buying something for that secondary purpose, you can do a lot better than this iffy thing.
5 or 6 amps is only workable if the Jalapeno is 5-7gh. The 3 chip Jalapenos need a 10 amp supply.
First time seen BFL actually help a customer in these forums without resorting to name calling first. FTC has made them be more polite one other good thing to come from this TRO.
More typically they just provide BS in a bag. But they charge you extra for the bag and the foam pitchforks. Whole threads full of zero customer service right here as an example:
Issues with your BFL products?
Post below. Seems to be a more than a few smoking units out there.
Gotta quote this one for posterity! Epic fail Bick... the guy bought 2 Jalapenos that were... wait for it... running TOO FAST! Damn dude, read!
That is more Bruce Peterson's speed.