Start the pork and aromatics: put the pork and water in a large pot and bring to a boil over medium-high heat. Skim off the foam that rises in the first few minutes. Add the onion and tomatoes, lower the heat to a steady simmer, and cook for 30 to 35 minutes, until the pork is tender and the tomatoes have softened into the broth. Lightly mash a few tomato pieces against the side of the pot to help them melt in.
Sour the broth: stir in the tamarind concentrate and the salt. Simmer for 2 minutes, then taste. The broth should be clearly sour before any vegetables go in. Add more tamarind a tablespoon at a time if it tastes flat.
Add the sturdy vegetables: add the daikon rounds and finger chilies if using. Simmer for 4 to 5 minutes, until the daikon turns slightly translucent at the edges.
Add the quick-cooking vegetables: add the long beans, eggplant, and okra. Simmer for 3 to 4 minutes, until the beans are bright green and just tender and the eggplant is soft but still holding its shape.
Season with fish sauce: stir in the fish sauce and taste again. You want sour first, then salty and savory. Add more fish sauce a teaspoon at a time if the soup tastes thin.
Wilt the greens last: add the water spinach and stir just until it wilts, about 30 seconds. Take the pot off the heat right away so the greens stay green.
Serve: ladle the soup into bowls with a piece of pork and a mix of vegetables in each. Serve with hot rice on the side and extra fish sauce at the table.