When did the FAA begin offering added-rating tests for flight instructors?
Could you decode your abbreviations for us. I just took all of the tests and I am not familiar with those abbreviations. 

Just to clarify for those who are not familiar with the knowledge tests. You need to take the Fundamentals of Instruction knowledge test (FOI) for all of the instructor certificates. You can take the Basic Ground Instructor (BGI) test, Advanced Ground Instructor (AGI), and Instrument Ground Instructor (IGI) if you want to get a Ground instructor certificate. To get your CFI certificate you need to take the Flight Instructor Airplane (FIA) test. CFII requires the AIF. There are separate tests for Sport Pilot Instructors. 

If you are adding a rating to an existing certificate, you can take an abbreviated version of the test, e.g. if you already have your CFI Airplane, then you can take the add-on test for gliders and only have to answer 25 questions rather than 100, and the questions will focus on glider operations assuming you already know the rest of the stuff.

Once you have any instructor certificate, you never have to take the Fundamentals of Instruction test again.

I don’t know when the short tests started, but if you look at Order 8080.6D which was published in 2003, you can see that short tests were available then. Since you had your CFI in 2009, you had the option of taking an abbreviated test for your CFII.