Heat oil in a large frying pan over medium-high heat. Add onion, season with salt, and sauté, stirring often, until just beginning to soften, 3 to 4 minutes.
Stir in mango relish. Add shrimp and stir to coat thoroughly. Lower the heat to medium, cover, and cook just until the shrimp curl tightly, 3 to 4 minutes.
Remove from heat; stir in lime juice and most of cilantro. Serve over rice, topped with remaining cilantro and more mango relish on the side.