Cook and stir garlic in a skillet over medium-low heat until fragrant, about 1 minute. Stir tomatoes, apples, and jicama into garlic; cook and stir until tomatoes are hot, 3 to 5 minutes.
Stir cilantro, chives, basil, and salt into tomato mixture; drizzle lime juice and vinegar over the top. Cook and stir until apples are juicy but still crisp and tomatoes are warm but still firm, 3 to 5 minutes. Drain some of the accumulated juices and transfer salsa to a bowl; refrigerate until chilled.