My mom's birthday is Dec 30, so going *on* her actual birthday isn't really something we want to do. One year we went from Jan 1-7 to celebrate her birthday, and she got a birthday button on the boat to Epcot when the CM asked "who was celebrating a birthday" (as opposed to "who has a birthday today"). The CM told her to make sure to get one in every park - obviously implying that she'd be celebrating her birthday the entire trip, not just the day of her birthday.
Also, as someone mentioned before, if you tell the CM making your ADRs it's a trip for a birthday or anniversary, they put that notation on *every* ADR, not just one on the day of that event. That also implies that your Disney vacation is meant to celebrate whatever event the *whole* time, not just one day.
my mom's birthday card/cake at Yachtsman - b/c the CM noted her birthday on our ADR