Sorry for the delay in posting – lots of work and other issues have come up. The Yerushalmi (Meg 7 in Vilna ed) raises a safeik which month of Adar is the “real” month of Adar and which month is the tosefes, the added month. The gemara writes that the nafka mina would be for the daily korban tamid (acc to girsa of Korban Eidah), which must be no more than one year old. Let's say an animal was born on 15 Adar. If the next year is a regular year, on 20 Adar the animal would be pasul for a korban because it is over a year old. If the year is declared a leap year, then if Adar I is the “real” Adar and Adar II is a “tosefes”, the animal is pasul. However, if Adar I is a “tosefes” and Adar II is the “real” Adar, then the animal is still kosher.
The S.A. paskens that if a child is born in a regular year, his bar mitzvah will be during Adar II of a leap year because Adar II is the “real” Adar. What if the child is born during a leap year on Adar I - would his bar mitzvah be in Adar I or Adar II? The MG”A (O.C. 56) paskens that the bar mitzvah should still be in Adar II, as the bar mitzvah always must occur in the “real” Adar. One of the MG”A proofs comes from a well known Yerushalmi in Kesubos. Chazal assume that a girl’s besulim will grow back if she is niveles before age three. If a girl’s birthday was on 15 Adar and she was niveles on 20 Adar, she is assumed to have lost her besulah status. However, if even on 29 Adar Bais Din declares the year to be a leap year, the girl would retroactively retain her besulah status because she has not yet reached her third year. (Many interpret this Yerushalmi to mean that B”D’s declaration does not just change the girl’s legal status, but changes reality and causes the girl’s besulim to return – this is a discussion for another time.) Just like the besulah is assumed to have not yet reached her third year until the date of her birthday in Adar II, so too, reasons the MG”A, a bar mitzvah boy does not reach the age of gadlus until his birthday is reached in Adar II.
Many Achronim (see R’ Akiva Eiger) disagree with the MG”A… IY”H more to come, and IY”H I will get more time to write : )