Tosefta על כתובות 50:16

Rabbi Shimon ben Gamliel says, "Just as the the presumptive status for the priesthood [is established by] the distribution of Terumah on the threshing floors (following Ketubot 25b:2, Steinsaltz tr.), so too, is the presumptive status for the Levites [established by] the distribution of the first tithe on the threshing floors. [However,] the distribution in the court does not [establish] for him the presumption of the priesthood (Ketubot 26a:7).

There are two presumptions [to establish a putative Kohen's status in the priesthood] in the Land of Israel: the Lifting of the Hands [for the Priestly Benediction] and the distribution [of Terumah] on the threshing floors (see Ketubot 25b:2). And in Syria, and until the places that the messengers of the new month would arrive (Rosh Hashanah 1:3), [a putative Kohen's status is established by] the Lifting of the Hands, but not by the distribution [of Terumah] on the threshing floors. And Bavel is like Syria. Rabbi Shimon ben Elazar says, "So too, in Alexandria, in earlier times when it had a [Jewish] court."