Cut each pork tenderloin in half. Mix together 1 cup of the salsa with the Worcestershire and vinegar.
Place the pork in a large resealable bag, and pour salsa mixture inside bag. Seal bag and refrigerate for six hours or overnight.
Preheat a gas grill to medium.
Arrange pork in the center of the grill; reserve the marinade. Lay the red onion slices on the cooler section of the grill. Cover grill and cook until pork is nicely browned underneath and onions are softening, about 10 minutes.
Turn pork and onions over. Baste pork and onions liberally with reserved marinade. Discard any remaining marinade.
Cover the grill and cook until the pork reads 150°F on a meat thermometer, about 5 minutes more. Transfer pork to cutting board and tent with foil, letting it rest for at least 5 minutes.
Chop the onion slices and transfer to a bowl. Add remaining salsa, apricots, parsley, lemon zest and avocado; season with salt and stir gently.
Thinly slice pork and generously spoon salsa over slices just before serving.