How to Make It
Stir together paprika, salt, black pepper, mustard, and cayenne in a small bowl. Rub pork pieces evenly with paprika mixture; refrigerate, uncovered, at least 1 hour or up to overnight.
Stir together ketchup, vinegar, molasses, and sugar in a small bowl; set aside.
Select SAUTÉ on a programmable pressure multicooker (such as Instant Pot). (Times, instructions, and settings may vary according to cooker brand or model.) Select HIGH temperature setting, and allow to preheat 2 to 3 minutes. Add oil. Place 2 pork pieces in oil; cook, turning occasionally, until browned on all sides, about 10 minutes. Transfer to a plate; repeat process with remaining 2 pork pieces.
Add onion, watermelon rind, and garlic to cooker; cook, stirring often, 3 minutes. Add watermelon flesh and ketchup mixture, scraping bottom of cooker pot to loosen browned bits. Press CANCEL.
Return pork to cooker; cover cooker with lid, and lock in place. Turn steam release handle to SEALING position. Select MANUAL/PRESSURE COOK setting. Select HIGH pressure for 60 minutes. (It will take 10 to 15 minutes for cooker to come up to pressure before cooking begins.) Let the pressure release naturally (float valve will drop). (This will take about 15 minutes.) Turn cooker off. Remove lid from cooker. Transfer pork to a plate, and shred using a fork. Set aside.
Let remaining mixture in cooker stand 5 minutes; skim fat from surface. Transfer mixture to a blender. Secure lid on blender, and remove center piece to allow steam to escape. Place a clean towel over opening. Process until smooth, about 30 seconds. Return sauce to cooker. Select SAUTÉ setting. Select HIGH temperature setting. Cook, stirring occasionally, until sauce is slightly thickened, about 10 minutes. Serve pulled pork with sauce, sliders, and pickled watermelon slices.