Remove the silver skin from the pork rib racks and pat them dry. Cut them into 2 to 3 rib portions.
Combine the paprika, chili powder, salt, cumin, black pepper, and cayenne pepper. Rub the mixture over the ribs.
Place a trivet in the Instant Pot and add the apple juice, vinegar, and Worcestershire sauce.
Stack the ribs on the trivet.
Lock the lid in place and turn the steam release valve (black venting knob) to the sealing position. Select the manual button, high pressure, and set the timer for 25 minutes. When the time is up, let the pressure release naturally for 12 minutes, then carefully turn the valve to the venting position to release the remaining pressure.
Preheat the broiler. Line a large baking pan with foil.
Arrange the ribs on the baking pan, meaty side up, and brush with barbecue sauce.