Amusingly i took FATs at Cranwell 2 days after you posted this thread!
I completed my application and had it sent by late August. Over a month later i was called upon to take my psychometric testing at my local recruitment office. Once i had passed that i was told my Liaison Officer would get in touch, and a week later i spoke to him. He then put me forwards for FATs which i then took about a month later.
Having unfortunately failed it, i was then told to retake a year later. So all i say is be glad you will probably have a while between now and the FATs.
I recommend for the best results, practice arithmetic and also remaining calm under pressure.
If you end up passing, i believe you take a second medical for Air Crew, then you go to AIB after meeting your liaison officer in person and if successful with that he will recommend you to the AIB.
Hope all goes well,
TheMau5e