Season pork with salt, paprika and garlic powder. Heat oil on the sauté setting of a 6-quart electric pressure cooker and brown the pork in batches for about 2 minutes per broad side.
Return all pork to the pot with onion, cider and stock, scraping the bottom clean. Lock the lid and cook on HIGH pressure for 60 minutes, then allow a 20-minute natural release before releasing any remaining pressure according to the appliance instructions.
Check that the pork pulls easily with a fork; if still firm, pressure-cook for 10 minutes more. Lift the meat out, discard large fat seams and shred, reserving the cooking liquid.
Simmer apricot preserves, mustard, vinegar, ketchup, water, black pepper and cayenne in a small saucepan for 5 to 7 minutes until smooth and slightly thickened. Set aside 1/4 cup for the buns.
Skim the pork cooking liquid thoroughly. Toss the warm shredded pork with 1/2 cup of the skimmed liquid and the remaining barbecue sauce until moist but not soupy.
Toast the cut bun faces briefly under the broiler. Spread with reserved sauce, divide pork among the buns and add drained pickled onions.
Close and serve one sandwich per person. Refrigerate any extra pork promptly in a shallow container and reheat cooked leftovers to 165°F.