Whisk the paprika, chili powder and cumin in a bowl. Season the turkey with 1 teaspoon salt, 1/2 teaspoon pepper and all but 1 teaspoon of the spice mixture. Heat 2 tablespoons vegetable oil in a large skillet over medium-high heat. Add the turkey thighs, two at a time, and cook until browned, about 3 minutes per side (reduce the heat if the meat is getting too dark). Transfer to a 6- to 8-quart slow cooker. Reserve the skillet.
Whisk the ketchup, cherry jam, 1/3 cup vinegar, brown sugar, mustard, molasses, chipotles and sauce, and soy sauce in a medium bowl. Pour 3/4 cup of the mixture over the turkey; set aside the rest for the barbecue sauce. Cover and cook until the turkey is tender and easy to shred, 7 hours on low or 4 to 5 hours on high.
Meanwhile, make the barbecue sauce: Add the onion, garlic and remaining 1 tablespoon vegetable oil to the reserved skillet and cook over medium heat, scraping up any browned bits, until softened, about 5 minutes. Add the reserved 1 teaspoon spice mixture and toast, stirring, 30 seconds. Add the remaining ketchup mixture and 1/2 cup water and simmer gently until the sauce is thickened but still pourable, about 10 minutes. Stir in the remaining 1 tablespoon vinegar. Strain the sauce through a fine-mesh sieve, pressing on the solids with a rubber spatula. Set aside until ready to serve.
Remove the turkey from the slow cooker, leaving the juices behind. Shred the meat, discarding the bones. Return the meat to the slow cooker and toss with the juices; season with salt and pepper. Keep on warm.
Serve the reserved cherry-chipotle barbecue sauce on the side.