Prepare the mojo: Heat the oil in a deep saucepan over medium heat. Add the garlic and cumin and cook until the garlic is fragrant and a pale golden brown, 1 to 2 minutes. Do not let the garlic brown too much, or it will become bitter. Stir in the lime and orange juices, salt, pepper, and oregano and ⅓ cup water. Stand back: The sauce may sputter. Bring the sauce to a rolling boil. Taste for seasoning, adding salt or cumin as necessary. Let cool to room temperature, then stir in the cilantro.
When ready to cook, brush and oil the grill grate. Arrange the tenderloins on the grill. Brush the onion slices with any excess marinade, skewer them crosswise on skewers or toothpicks, and place on the grill. Grill the pork and onions until cooked to taste. The meat will take 3 to 4 minutes on each of its four sides, 12 to 16 minutes in all for medium. To test for doneness, insert an instant-read meat thermometer in the thickest part of the meat. The internal temperature should be about 160°F. Rotate the tenderloins 90 degrees after 2 minutes on each side to create an attractive crosshatch of grill marks. The onions should be nicely charred after 4 to 6 minutes per side.
Transfer the tenderloins to a cutting board and let rest for 3 minutes. Slice the tenderloins crosswise on the diagonal. Fan out the slices on plates or a platter and top with the unskewered grilled onions. Spoon the reserved mojo over them, garnish with the orange sections, and serve at once.
For absolutely carefree cooking, grill the tenderloin using the indirect method. You’ll need to allow 30 to 40 minutes of grilling time at medium heat.