Combine first 7 ingredients in a medium bowl, and set salsa aside.
Peel shrimp, leaving tails on; devein. Toss shrimp and onion with oil in a large bowl, sprinkle with Jamaican Jerk Rub, and toss to coat. Grill shrimp and onion over medium-high heat (350° to 400°) 6 minutes, or just until shrimp turn pink, turning once. Chop onion and add to salsa mixture, stirring gently. Serve shrimp with salsa.