They were both in the institute. The "older brother" is 18 so he had to leave. He just didn't tell sumire where he went or whats he doing. Sumire is 17 so hes still in the institute which is why theyre worried he hasnt come back yet and contacted mizuki to ask sumire where he is.
THE ONE WHO'S IN THE INSTITUTE IS SUMIRE??????
I always assumed it was the brother...