Yes, the Goblins are native to the Underworld. So are the Stygians. Both of them can build settler units underground and on the surface. The Buteo are another race that has two options for building settlers, though theirs is the surface and the clouds.
It's one of the perks of playing these specialty races that you have multiple options for building settlers. It's also handy for exploration, since your underground Goblin miner (settler) could be quite far away vertically from your surface Goblin miner. ToT is a game where you constantly have to think three-dimensionally on a 4-level map, so you don't put crucial units and cities in each other's way.
This is why Sorcerers are so handy - they can teleport to all levels so you can have a look around. They have limited movement, though, and have to end their turn in a city or on a platform, or they'll crash. In the initial turns of a game, they're very handy for scouting good places to build cities and seeing where your enemies are, if they're close enough.
You should be able to build Goblin miners in both underground and surface cities, as long as your cities aren't built on tiles like bedrock, tunnels, or other impassable terrain.
