I travelled through JFK using AP. There is a slightly different immigration procedure. When you land at JFK and go through the immigration line, there will be a guy asking whether you are a citizen/PR or a visa holder. You should tell them you have an AP. He will make you stand in a seperate line which is amongst the Green Card lines. When you go to the counter, the immigration officer will take your passport and AP, put it in an envelope and ask you to follow him into a seperate room. The AP processing is not done at the counters, so you need to go to that special room. There is nothing to be worried about, that is a normal procedure. You will be then asked to either wait outside the room or come and sit in the room, depending on how crowded the room is. There are a few counters in the room. You just wait there until your name is called. When called, you go up to the counter. The person at the counter will stamp your passport and thats it, you are on your way out.
The scene inside the room might look scary, but you don't need to be worried about it. Usually, they take people those people inside the room who dont have proper immigration documents. You'll see people being questioned inside the room. But it so happens that the AP processing is also done in the same room.