There's quite a mix of electronics in a UPS that could react in different ways to a power surge on the input. The general theory of operation is that they protect your hardware, "falling on the sword" if necessary. This is the case with your computer, I think it's fair to say your computer would be emitting the smoke if you had not had a UPS or surge suppressing power strip between it and the outlet when they popped the power wires.
Normally electrical "events" like this would be fairly brief, a bang or a pop or a buzz, some smoke, maybe a hiss or melting plastic, and would calm down in a few minutes. But since the UPS has batteries in it, it can supply "fuel to the fire" and keep things smoking until the batteries discharge. Be careful when opening it up, there are 1 or 2 lead acid batteries in there that may not be in the best of condition. They're often on their sides, which for normal lead acid batteries is a bad idea, but these are normally sealed with caps. These caps may not be in place if there's been a fault, so the batteries could leak hydrochloric acid. It won't melt your hands like in the movies, but if you DO get any on your skin, wash it off IMMEDIATELY, and don't let any get in your eyes or on your clothes for that matter.
Once the batteries are disconnected/removed, it shouldn't smoke for more than a few more minutes, assuming it's not ON FIRE or smoldering internally. I saw a video one time of a UPS sitting in a parking lot, running, providing power, and on fire but I can't find it right now. Apparently UPS (the shipper) has a lot of videos of their fires up on youtube right now. (??)
I work for the Department of Redundancy Department