About a year ago, Junior Nyong’o took a call from the director Saheem Ali. Nyong’o had recently graduated from drama school and Ali, an associate artistic director of the Public Theater and a family friend, had phoned to offer him a job.

Would he like to play Sebastian in a production of Shakespeare’s “Twelfth Night,” which would reopen the renovated Delacorte Theater in Central Park? Nyong’o accepted immediately.

But he had one question. Sebastian is an identical twin. Who, Nyong’o asked, did Ali have in mind to play Viola, his sister?

“Meeeeeee!” said a woman who was suddenly on the line. He knew that voice — it belonged to his sister Lupita Nyong’o.

“I kind of freaked out,” Junior Nyong’o recalled. He was speaking, calmly now, on an afternoon late last month, before a rehearsal for “Twelfth Night,” which is in previews and opens on Aug. 21. Brother and sister were seated on a sofa in a downstairs lobby at the Public’s rehearsal space, in matching haircuts — shaved on the sides and lightened at the tips. She wore a small star as a pendant. He wore a large one.

The two weren’t often in rehearsal together. The structure of “Twelfth Night” keeps the twins apart until an emotional reunion at the play’s end. A few days earlier, I had watched them rehearse that scene. With Ali standing by, they worked out the blocking.