In a medium saucepan over medium-low heat, heat 1 tablespoon of the oil. Add the onion and garlic and cook for 5 minutes. Add the coriander, mustard, and cumin and cook until the onions begin to turn golden, about 8 to 10 minutes. Add the tomatoes, vinegar, and sugar and stir. Increase heat to medium. Cook, stirring occasionally, until the tomatoes are softened but still retain their shape, 15 to 20 minutes. Remove from heat and season with the salt and cayenne pepper.
Meanwhile, heat the remaining oil in a large skillet over medium heat. Add the shrimp and cook, turning once, for 2 minutes total. Add the wine and cook for 1 minute. Cover, remove from heat, and set aside until the shrimp are pink and cooked through, about 5 minutes. Divide the rice among individual plates and top with the shrimp and chutney.
Tip: You can make the chutney ahead of time and refrigerate it for up to 2 weeks. Reheat it over low heat.