FAST works differently in that platoons work on a JORT cycle. Receiving, buildup, deployment, leave/training, deployment, out process. These cycles work over the course of 2 years with each platoon checking in and checking out at the same.
When I was in MCSFCo the overseas platoons worked differently in that they were permanent duty stations and not forward deployed platoons, with the exception of a single FAST platoon that would rotate through. Overseas commands had new checkins came as needed after completion of someone elses two year time. I think that it's different now and there are no more permanent Marines in Rota/Bahrain except HQ.
Why they didn't let you screen at the end? Could have been where the location of FAST (Hampton Roads area depending upon company; either Norfolk or Yorktown) and where screening events are (Lejeune or Quantico) or shitty leadership. I'm a beliver it was a combination of the above.