In a bowl, whisk together the red wine vinegar, lemon juice, and Dijon mustard until combined. Slowly drizzle in the olive oil while whisking constantly to create an emulsified vinaigrette. Add the Italian seasoning, salt, and pepper, and whisk until the dressing is smooth and well-combined. I like to taste and adjust the seasoning at this point—a pinch more salt can really brighten the acidity of the vinegar and lemon.
Bring a large pot of salted water to a boil and cook the fusilli according to package directions until al dente. Drain the pasta in a colander and rinse briefly with cool water to stop the cooking process. Let the pasta cool to room temperature before assembling the jars—warm pasta will wilt the arugula and make the dressing separate.
While the pasta cools, cut the chicken into 1/2-inch cubes, halve the cherry tomatoes lengthwise (this helps release their juices into the dressing), and prepare the black olives and arugula. Having all components ready before assembling makes the jar-packing process smooth and efficient.
Divide the dressing from Step 1 evenly between jars, filling the bottom of each jar. This prevents the greens from getting soggy. Layer in the following order: cooked pasta from Step 2, cubed chicken, black olives, and halved cherry tomatoes. Top each jar with the arugula. Pack the ingredients down gently but firmly to fit everything into the jars without crushing the arugula. I find that applying steady, even pressure helps compress everything nicely while maintaining the layered structure.
Close the lids tightly on each jar and refrigerate until ready to eat. The salad will keep for up to 3 days in the refrigerator. When you're ready to serve, shake the jar vigorously for 10-15 seconds to mix all the layers together and distribute the dressing evenly throughout the salad.