Prepare a medium-hot fire in a charcoal grill or preheat a gas grill on medium-high.
Remove the tenderloins from the refrigerator 20 to 30 minutes before grilling and place them on a large, rimmed baking sheet. Rub the pork on all sides with olive oil. Liberally season the tenderloins on all sides with the spice rub.
While the grill is heating, make the salsa: In a bowl, combine the nectarines, onion, cilantro, jalapeno chile, lime juice, honey, salt, and red pepper flakes. Stir to combine. Set aside until ready to serve.
To create a cool zone, bank the coals to one side of the grill or turn off one of the burners. Oil the grill grate. Place the tenderloins directly over the medium-hot fire. Grill the pork, turning to sear on all sides, for about 8 minutes.
Move the tenderloins to the cooler part of the grill, cover, and grill until the meat is slightly pink in the center, or an instant-read thermometer inserted into the thickest part of a tenderloin registers 145°F, 8 to 10 minutes longer.
Transfer the pork to a cutting board and let rest for 5 minutes. Cut the pork on the diagonal, across the grain, into ½-inch-thick slices and divide among warmed dinner plates. Put a large spoonful of salsa alongside the pork. Serve immediately.