You are required to demonstrate proficiency in a complex aircraft on your initial CFI checkride.
You're only required to demonstrate complex proficiency on your initial "airplane" CFI ride.
If you do the CFII first "Flight Instructor - Instrument", there's no complex requirement in the PTS.
Not sure if there's an advantage or disadvantage to doing the CFI ratings in a particular order. Either way, you either have the knowledge and skills and can teach it, or you don't.
Some people seem to think doing the MEI, CFII, CFI is "easier"...or doing it CFII, MEI, CFI is "easier" or whatever...it's not. They're all instructor checkrides. I just added my MEI not far back and even though I had the CFI/CFII, it was no joke. There were fewer tasks and areas of operation required to be on the test, but I had demonstrated them at least once anyway...same thing applies whether you do the MEI first or the CFI, CFII, etc.
For what it's worth, we do the CFII, then MEI then CFI...if a student doesn't want the MEI, they can demonstrate complex proficiency in the duchess and do the maneuvers in the 172...check the PTS, the complex requirement isn't category
and class...it's just category. If you're Commercial with SEL and MEL ratings, you can do the "complex" portion of the checkride (takeoff and landings - can you remember to toss the gear?) in either/or.
-mini