Slice the cucumber crosswise into 12 1-inch-thick rounds. Scoop out the center of each to form a cup.
In a bowl, stir together the yogurt, tahini, lemon juice, cumin, and garlic. Season with salt and pepper to taste.
Halve each tomato and use your fingers to scoop out and discard the pulp and seeds. Dice the halves, reserve 2 tbsp., then stir the rest into the yogurt mixture.
Distribute the tomato filling evenly among the cups. Top each with a few pieces of the reserved tomato.