Well, there's no reason for it to be specific to arid regions (tombs and mummies can pop up anywhere, after all), and being DF, it would be very unlikely for the genie to be benevolent. Originally, a genie (or djinni) was simply a demon, and the idea of a genie bound to a lamp (or a ring, or any other item) was based around the idea that a powerful sorcerer was able to capture it and force it to work for them.
This might fit well with DF demons, though, especially now that we have binding a demon with its true name. Perhaps one of the things you can do with a demon's true name is bind it to an item so it comes when it is summoned. Once more complex requests and commands are implemented, you can send a bound demon on missions just like anyone else, and it would be forced to obey (which is closer to the original idea of 'wishing'; a djinn commanded to give you money couldn't simply create money for you from nothing, but it could travel to the ends of the earth and bring back gold and jewels). Maybe this could even happen in worldgen, so it would be possible in older worlds to find a legendary artifact with a demon bound to it. Of course, anyone who tries to summon the demon from the item without knowing its true name is probably going to have a bad time...
Maybe sorcerers could find a way to summon new demons from the underworld by learning their true names and use a summoning circle to bind them. That way you could have more than one or two per world. They could record the demons' names in books, you would need to find both the book and the item in order to command the demon yourself. It would also be nice if there were different 'tiers' of demon; a sorcerer could summon lesser imps easier than the powerful top demons.