Combine 2 cups water, vinegar, turmeric, and 2 teaspoons salt in a bowl or large jar. Add eggs; chill 4 to 8 hours, turning occasionally to "stir." Drain eggs; pat dry with paper towels.
Heat a small skillet over medium. Add curry powder and cumin; cook, stirring constantly, until fragrant, about 1 minute. Cool.
Cut eggs in half crosswise; carefully remove yolks, and place in a mini food processor. Cut a sliver off each rounded bottom of egg white (so eggs will sit flat); place egg whites on a platter. Add mayonnaise, yogurt, curry mixture, and remaining 3/8 teaspoon salt to processor; pulse until smooth, adding 1 or 2 tablespoons water if mixture becomes too thick. Add chives; pulse to combine. Divide filling evenly among egg whites; top with additional chives, if desired.