Preheat oven to 425 degrees F. Set a wire rack on a rimmed baking sheet and coat with cooking spray.
Whisk 1/4 cup water, 4 tablespoons vinegar and 1 tablespoon each tamari and brown sugar in a medium bowl. Add cabbage and radishes and toss to combine. Set aside, tossing occasionally.
Meanwhile, combine the remaining 1 tablespoon vinegar, 3 tablespoons each tamari and brown sugar, gochujang, garlic and ginger in a small saucepan. Bring to a simmer over medium-high heat. Cook, stirring occasionally, for 2 minutes.
Whisk the remaining 1/4 cup water and cornstarch in a small bowl. Slowly add the cornstarch mixture to the sauce, whisking constantly. Cook until thickened, about 1 minute.
Pour half the sauce into a medium bowl and add tempeh; gently toss to coat. Transfer the tempeh to the prepared rack. Bake until the sauce is tacky, about 15 minutes. Return the tempeh to the bowl and add the remaining sauce. Gently toss to coat.
Divide rice among 4 bowls. Transfer the pickled vegetables to the bowls using a slotted spoon; drizzle with the liquid, if desired. Top with the tempeh and sprinkle with cilantro.