In 5- to 6-quart pan over high heat, bring 3 quarts water to a boil. In a food processor, whirl garlic and chili until minced. Add onion and pulse until minced. Scrape into a large bowl and stir in cucumber and salt.
Cut an X in the bottom of each tomato and immerse in boiling water until peel begins curling back, about 30 seconds. Rinse under cold running water until cool. Set a strainer over bowl with onion mixture. Working over strainer, pull peels off tomatoes and cut out and discard cores. Gently squeeze juice and seeds out of tomatoes. Press seeds to extract juice; discard seeds. On a cutting board with a juice well, mince tomatoes; pour any juice that collects into strainer. Add minced tomatoes to bowl with onion mixture.
In a small bowl, mix tamarind concentrate with 1/4 cup warm water. Stir into tomato mixture, along with cilantro, mint, and ginger. In a 6- to 8-inch nonstick frying pan over medium heat, stir ground cumin until fragrant, 2 minutes; add to soup. Cover and chill until cold, at least 1 hour, or up to 1 day.
Ladle soup into bowls; top each serving with about 1/4 cup yogurt. In a 1- to 2-quart nonstick pan that has a tight-fitting lid, combine oil, cumin seeds, mustard seeds, and nigella seeds. Set over high heat and stir until spices begin to pop, 30 seconds to 1 minute. Cover and shake vigorously until popping begins to subside, 1 to 2 minutes. Spoon hot seeds equally over soup.