The "style" section of the enotes study guide on Hughes' play "Mulatto" identifies three things that might help to answer your question: setting, language, and foreshadowing.
The setting is relevant because the story takes place in the American South. Slavery has ended (there are automobiles in the play, for example), but the strict racial hierarchies are still firmly in place. The plantation owner is white, his mistress is black, and their mixed-race children are treated better than the black workers (e.g. education and mobility) but not as full equals of the whites (e.g. the whole plot revolves around Robert's refusal to "stay in his place").
Language in the play also fits into the discussion of setting. The blacks mostly speak in a strongly marked dialect. (The whites, on the other hand, don't speak in an entirely realistic dialect. Their English is often too formally correct to seem real to me as a reader.) The study guide elaborates: "Robert becomes a threat to the status quo. Since he has been educated, he talks like a white man does, in clear, grammatically correct English."
Foreshadowing is found in the warnings and concerns early in the play about Robert's need to "stay in his place." You might also look at Cora's dream (which warns of trouble to come) and the references to Norwood's pistol.