My DS got his button in MK. It had a picture of the castle on it. He was told to go to City Hall to pick it up and wear it all around WDW because "magicial" things will happen. And it did......
My DS got all the birthday buttons in June. MK and Disney-MGM are the same, but we got one of each. At AK, my DD got a button about conservation. I guess the CM felt bad for her, not being there on her birthday.
Picking up the birthday pins at guest relations is part of the fun! At Disney-MGM, the CM went back in the office to see if anyone back there could come up to visit with my DS. Everyone was too busy playing fetch with Pluto! But they did sign a really nice birthday card for my son. With his name and everything! My DS got a phone call at AK. It depends on the CM at the desk when you go in, what they will do for you.