The rama seemingly contradicts himself in certain halachas during adar aleph and adar beis. He writes a bar mitzva boy isn’t barmitzvah untill the date in Adar 2 but a yartzeit should be commemorated in Adar aleph: What is his reasoning? Which Adar is the real adar or is it both?
The Rema indeed rules that concerning bar mitzvah, a child born on a regular adar becomes bar mitzvah (in a leap year) in adar beis (55:10), whereas concerning a yartzeit he rules that the day is commemorated (in principle) in adar aleph (568:7). There are two possible approaches, based on two sources mentioned in Rema’s text, for resolving this seeming contradiction.
1) Maharm Mintz (9) writes that the true Adar is the second Adar month, and this is therefore the month for bar mitzvah. However, the yarteit is observed in the first month, because it depends on the count of twelve months, which is when the judgment [of the wicked] ends, and the day that is rei’a mazlei. This would be true for the first year after the parent’s death, and the same day would be observed for every year.
2) According to Maharil (104-105), the age of the child is determined by the second Adar month, because a shanah temimah is required, however, the yartzeit follows the first Adar month, because this is only an expression of one’s grief.
See Kol ha-Torah, vol. 58, p. 346ff, where this question is addressed at length.