The 12 students and staff who were taken to hospital or received medical treatment have been moved to Nairobi Hospital, with injuries ranging from bruises to broken bones.
Five students and staff who were not in the minivan had been cleared to leave and were travelling back with their families, said Mr Hollister-Jones.
They were expected to speak at a press conference at the college on Wednesday.
A second group would be leaving a few days after, while one student, Aneka Jones, would probably stay behind in hospital after suffering a dislocated hip and fractured pelvis in the crash.
Mr Hollister-Jones said her parents had flown over to support her.
The driver of the minibus and inspirational figure in the college project to build the Ark Quest Education Centre, Nairobi lecturer Christopher Mmata, was also killed.
College principal Eoin Crosbie said all of the group were "progressing well" and were "in good hands".