We were just at Ohana last week and the table next to us had a child and an adult with birthday pins. The staff came over and clapped and sang to them, the characters crowded around and danced and clapped as well. I didn't see any cupcake or anything presented to them.
We went to Crystal Palace our first morning in the parks and my daughters each had on their "1st time at WDW" pins (we got them when we activated our APs at DTD the night before as our ADR was so early). The waiter mistook them for birthday pins and brought the girls each a birthday card signed by all the characters and a cupcake (for breakfast!?). When he started to set them down, I pointed out that it wasn't their birthday, and that's when he did the double take on their pins.....he said well, they get to celebrate it anyway...and proceeded to have Pooh and Tigger dance and the staff sing to them. The girls were thrilled, because their birthday is in the summer and we'd never be at WDW for it, so they loved that!
We've seen other people in restaurants with the birthday pin and not seen anything happen for them, so I don't know if each restaurant treats things differently, or if you have to either have an observant waiter or make a point to tell them about it.
I'd say if you want to be sure that they do something special, that you have a note put on your ADR (when I was making ADRs they asked if there was a special occassion being celebrated)....but then also tell them when you check in at the restaurant, and maybe even tell your waiter. I can only imagine how many people are celebrating a birthday at WDW on any given day, so it might be easy for it to be overlooked by busy staff. I've read many people saying that notes on ADRs were ignored (including paid for special cakes) and that they've had to remind staff of their celebration. If you want it to be extra special/surprise like for the kids, then I'd suggest checking in by yourself while the kids wait a little way away with others and let them know, and then perhaps getting up from the table, either to get buffet food, or on the excuse of a bathroom trip and finding your waiter and letting them know. I'm sure they'll do something special if they know...it's the making sure the word gets to the right person that you may have to work to ensure. I don't know if every restaurant has birthday cards like CP did, so if you want to be sure your kids get one of those, you might buy some before you leave and tuck them into your purse when you go and ask your waiter to get them signed. I know that even though their birthday is still 5 months away, my girls loved getting a card from Pooh and friends....and they have been sitting on the top of the TV since the day they got them. Now, just to be sure they get packed when we leave!