Lay the cubes of pork in one layer and sprinkle, on both sides, with salt, liberally. (I used about 1 1/2 teaspoons of salt.) To a medium pot or Dutch oven, set over medium-high heat, add 2 tablespoons of oil. When the oil glistens, it's ready; using tongs, add the cubes of pork, in one layer, and sear on both sides for 30 seconds to a minute, or until golden brown. Depending on the size of your pot, you may need to do this in two batches. Remove pork and set aside.
Bring heat down to medium and add 1/2 of the diced onion; cook until translucent, about 3-5 minutes. Next, add the garlic cloves, ground cumin, chile powder, and toss. Cook for about 30 seconds more.
Add the pork back to the skillet and in squeeze the orange and half of the lime over the meat. Pour enough water to slightly cover the meat and turn the heat to medium-high until it reaches a simmer. Once it's at a simmer, bring heat down to medium-low. Cook, uncovered, for 3 hours, adding water frequently. The meat is ready when it's easily shreddable.