I am one of the aliens that went through the process. When I did it the website was the same, but it was the DOJ responsible for the background check instead of the TSA. I filled out the application (13 pages I think) and then about 2-3 weeks later they said I had preliminary approval, so I drove to FlightSafety in Toledo to get fingerprinted...you can do it at any US police station, but I figured having someone at FlightSafety overseeing the process might ensure everything gets sent where it should. About 2 weeks later I got the final approval to begin training. You have to be very thorough filling it out...in the employment history section I neglected to put 'unemployed' during a two week stretch between graduating and starting a new job...they rejected my application and I had to send a new one in...added about three weeks onto the whole process.
If you are type rated on an aircraft over 12,500 you can go through expedited screening. The new rules also allow for some sort of treatment if you hold an airport restricted area pass.