The four people in rasputin's bunker are the four from the ishtar academy.
That would be the theory... They all became Exos as it was more efficient to Time travel/enter Vex networks. Cayde first, (Clovis Bray paid for him to become exo, and cleared all debts). Then he returned to Ishtar and eventually everyone did, though Maya was 40+ years later as she was holding out due to her love for Chioma.