Riggwelter is obviously "on scene" and so has the latest information. When I was there it was pretty much the same. I was hired for the 737-200 (F/0).
I was already typed in the airplane with 6,000 hrs and a Master's degree.
When I got there I was also "assigned" the Twin Otter and then the CE-550.
I was sent to the States for the CE-550 S/P type authorization. The DHC-6 training was done locally. The CE-550 is only used for aerial photo missions. The twin otter was used for mostly medivac flight out of Shaybah. The pilot group when I was there consisted of Saudi nationals followed by U.S. citizens and Canadian citizens. There was 1 French national (U.S. green card holder). Everyone must have U.S. licenses and a medical. BTW you have to do your medical with the Dr. in Dhahran. So if you have something medical and have "Santa Claus" MD--think again!!
I did all my 737-200 training in DFW before heading to DHA. When you get there you train in the aircraft again--since money is no object, nor is ATC congestion. We went out in the 737 and did steep turns and stall recognition.