Toss the squash with 2 tablespoons olive oil on a baking sheet and spread in an even layer. Season with 2 teaspoons rosemary, and salt and pepper. Roast, stirring once halfway through, until the squash is just tender and golden, about 20 minutes. Remove from the oven and cool until just warm, about 15 minutes.
While the squash is roasting, peel 3 tangerines and slice them crosswise into 1/2-inch-thick rounds, removing any seeds. Juice the remaining tangerine and whisk the juice together with the remaining 2 tablespoons olive oil and remaining 1 teaspoon rosemary. Season the dressing with salt and pepper.
Combine the warm squash, the spinach, tangerine slices and cranberries with the dressing and toss gently to coat. Divide among salad plates.