Rinse the capers under running water and leave them to soak for half an hour. Cook the pasta in a large pot of lightly salted boiling water for one minute less than the time indicated on the package. Drain the pasta, add one tablespoon of olive oil, stir, let cool and refrigerate covered with plastic wrap.
In the meantime, cut the cherry tomatoes in half or in quarters depending on size. Drain the tuna and break it into large pieces. Cut the mozzarella into cubes.
In a large salad bowl, mix the cut tomatoes, pitted olives, tuna, mozzarella, capers and roughly torn basil leaves. Dress everything with the remaining oil, adjust the salt and pepper and mix thoroughly.
Take the pasta out of the refrigerator and toss with the other ingredients in the salad bowl. Finish with the lemon juice. Let rest for another half hour before serving.