Heat butter in a large skillet over medium. As soon as butter stops foaming, add ginger and scallion whites and cook, stirring, until fragrant, about 1 minutes. Add tomatoes and cook, turning gently with a large spoon, until tomatoes are juicy and just warmed through, about 2 minutes. Add soy sauce and toss to combine. Taste and season with salt, if needed. Top with scallion greens.