Combine the first 5 ingredients in a large bowl. Combine mayonnaise, rind, and juice in a small bowl, stirring with a whisk. Add mayonnaise mixture to crab mixture; toss gently to coat. Arrange tomatoes on a serving platter; drizzle with oil. Sprinkle tomatoes with salt and pepper. Mound crab mixture over tomatoes. Sprinkle with basil leaves.