Why does Rashi quote Vayikra 23:39 as the source for Ibur Shana ("מכאן שנצטוו לעבר את השנים"), as opposed to Devarim 16:1 quoted by the Rambam in Hilchos Kiddush Hachodesh 1:1 ("והשנים שאנו מחשבין הם שני החמה שנאמר שמור את חדש האביב"). Rashi in Devarim also mentions Ibur Shana, but not with the same language. This is a follow up question of What is the biblical source for leap years?
Rashi on Chumash does not make definitive statements that here, as opposed to there, is the decided halachic source for some law. Rather, his chosen role is to channel midrashim in order to show how Chazal understood the pesukim, in a manner that is consistent and runs through the each pasuk in turn.
Often, while doing this, he acts as a conduit for one primary midrashic source. (See here about Sifrei and a switch to Tanchuma within sefer Bamidbar. Or here, where he channels Mechilta on sefer Shemot, even though it ends up like a position against halacha, of Bet Shammai against Bet Hillel.) Rashi's primary midrashic source for sefer Vayikra is Toras Kohanim, that is, the Sifra. While other sources are interjected, see the perek in full here at Chabad.org with its repeated running references to Toras Kohanim.
So it is not Rashi vs. Rambam as to the source pasuk. Rashi in his commentary on Vayikra channels the primary midrashic material on Vayikra, and Rambam in his halachic work channels a different earlier (Talmudic?) source.