Bring a large pot of salted water to a boil. Prepare a bowl of ice water and set next to the stove. Add the green beans to the pot and cook until crisp-tender, 4 to 6 minutes, and then plunge them into the ice water to stop the cooking. Once cool, dry the green beans completely and season with salt.
Combine the tangerine and orange zest in a small bowl and set aside. Slice the tops and bottoms off the oranges and 2 of the tangerines using a sharp knife and set on a flat surface. Remove the skin and pith from each, and then carefully slice in between the membranes to release the sections into another small bowl, catching the juice. Drain the juice into the bowl with the zest. Juice the remaining 2 tangerines into the same bowl, and discard the seeds.
Heat 1 tablespoon of the olive oil in a large skillet over medium heat. Add the shallots and cook until tender and beginning to brown, 5 minutes, and then pour in the zest and juice, bring to a simmer and cook until the liquid is almost completely absorbed, 3 minutes. Transfer to a large bowl. Stream in the remaining 3 tablespoons olive oil while whisking constantly, and then season with 1/2 teaspoon salt and 1/4 teaspoon pepper. Toss in the green beans to combine and taste again for seasoning. Arrange on a serving plate and garnish with the orange and tangerine sections. Serve warm or at room temperature.