AC automatically turns on

If I turn off ac, then turn off the car.......

Why does the ac turn on automatically when I start car.

Mine stays the same as I left it when I shut it off. Not sure why your 7 does that, maybe you have it saved that way in the personal profile settings, or it's in you key's memory.

Maybe it is in my keys memory.... I checked the personal profile and did not see anything.

My 750li does the same thing; AC automatically comes on when car is started

I shut off the ac then shut off car and fan still turns on.

is it warm out?

If the a/c was on and then turned off, and then the CAR is it turned off for a certain amount of time, the a/c will be back on next time it starts; same logic with the heater. I guess BMW Environmental Control System engineers believe there is a need to always have climate control/circulation all the time.
Speaking of climate control I prefer the old 7 series. You could control the percentage of air coming out of both the upper and lower regions at the same time. Now you can only have upper or lower, not both. During hot weather I prefer most of cold air blowing from above, but also like a little (about 20%) of cold air towards foot well. Can't do that with post 2009 7 series. Go figure,,,,