Place phyllo shells on a baking sheet and bake until lightly crisp, about 5 to 6 minutes; cool to room temperature.
Meanwhile, halve tomatoes lengthwise and use a teaspoon to scoop out and discard pulp and seeds; dice tomatoes and place in a medium bowl. Add remaining ingredients to bowl; toss to mix and coat. Fill each shell with about 1 tablespoon tomato mixture; garnish with dill.