Combine tomatoes and 1/2 tsp salt in bowl and toss to coat; transfer to colander and let drain in sink for 30 minutes.
Whisk oil, vinegar, lemon and juice, 1/2 tsp salt, and 1/2 tsp pepper together in large bowl. Add nectarines, shallot, and drained tomatoes to dressing and toss gently to coat. Season with salt and pepper to taste. Transfer to platter and sprinkle with mint. Drizzle with extra oil. Serve.
