Preheat a pot of water to boiling for cooking pasta.
Cook pasta according to package instructions until al dente, then drain and rinse with cold water.
In a large bowl, combine cooled pasta, celery, red onion, cherry tomatoes, and parsley.
In a separate small bowl, whisk together mayonnaise, Dijon, lemon juice, vinegar, minced garlic, salt, and pepper to make the dressing.
Pour dressing over the pasta mixture and toss to coat evenly.
Add drained tuna and gently mix to combine without over-mashing.
Chill in the refrigerator for at least 30 minutes before serving to let flavors meld.