the fan should come on anytime the car gets to the heat where it needs it. i had a car that did that, it was a little older than yours though and i had to just stop using the air because i couldnt find the problem with it, all i could guess was something in the elctrical that wouldnt allow the fan to work with the a/c.
yes it should come on as soon as you turn on the a/c unit on it,if its not working check the fuse circuit and the relay for the cooling fan,that would be the problem with it over heating,its usually the relay for the fan that makes it stop working,good luck with it.