Related do Terumot 3:13

A worker who separates terumah from the threshing floor [without explicit permission], his terumah is not [valid] terumah, but if the landowner said to him, "gather together [the produce] of my threshing floor," his terumah is [valid] terumah, as [the produce on] the threshing floor may not be gathered together unless terumah has [first] been separated.

But orlah and diverse crops (kilayim) of the vineyard (see Orl. 3:7) are [treated] the same for Gentiles in the Land of Israel, in Syria, and outside the Land (cf. Avodah Zarah 54b:6). But Rabbi Yehudah says, the [laws of] the fourth-year vineyard do not [apply to] a Gentile in Syria. And the Sages say, they do apply (Ter. 3:9). Said Rabbi Yehudah, it so happened with S'gabion (שְׂגַבְיוֹן not שביון) the head of the synagogue of Achziv, that he had purchased from a Gentile a fourth[-year vineyard] in Syria and had paid [the Gentile] money for it. And he came and asked Rabban Gamaliel, who had been passing from place to place [about whether such a vineyard is liable]. And [Rabbi Gamaliel] said to him, "Wait until [this situation] becomes [the subject of] halachah" (i.e., Rabban Gamaliel did not know the answer). They [the Sages] said to him [Rabbi Yehudah], "This is no proof [that such a vineyard is not liable]. Not only that, but [Rabban Gamaliel later] sent him [S'gabion] in the hand of a deaf-mute messenger (alt., "a secret message," see Lieberman), [stating,] 'What you did, you did, but do not teach [others] to do so.'"

From what time may they (i.e., the chaverim workers specifically designated to tithe the winepress, see Ter. 3:4 and Bartenura there) take terumah from the winepress [on behalf of the am ha'aretz owners]? After they tread on the [grapes in the vat both] vertically and horizontally. From what time do [the am ha'aretz owners enter and] render the winepress impure? Beit Shammai say, "After first tithe is removed [by the workers]." Beit Hillel say, "After second tithe is removed." Said Rabbi Yehudah, the halacha is according to the words of Beit Shammai; however, the multitudes have become accustomed to act according to the words of Beit Hillel. And the Sages say, [the workers] take out terumah and tithes and [the owners] immediately [enter and] render the winepress impure.

One who says, "The terumah for this pile [of produce] is in the north," then [the result would be that] the entire half nearest the north is rendered a medummah (a forbidden mixture of terumah and chullin), the words of Rebbi. But the Sages say, [what he can do instead] is arrange the pile in the form of the letter "chi" (similar to an X, to minimize contact between terumah and chullin). Rabban Shimon ben Gamaliel says, he can take the terumah from the northernmost [part].

One who takes terumah before first fruits, first tithe [before] terumah, or and second tithe before first tithe, even though he transgresses a negative commandment, what he did is done. [If he prematurely took] first [tithe], it may not be eaten before second [tithe] is taken out of it. [If he prematurely took] second [tithe], it may not be eaten before terumah is taken out of it. And terumah does not prevent the the giving of first fruits. Similarly, [if] one makes starter dough from untithed produce, whether he took challah before terumah, or whether he took terumah before challah, what he did is done. Challah may not be eaten before terumah is taken out of it, and terumah may not be eaten before challah is taken out of it.

[If] he was going to separate terumah at the appropriate time of separation, and he said, "Behold, this is first tithe," then behold, it is first tithe. [If] he was going to separate first tithe at the appropriate time of separation, and he said, "Behold, this is second tithe," then behold, it is second tithe. [If] he was going to separate second tithe at the appropriate time of separation, and he said, "Behold, this is poor person's tithe," behold it is poor person's tithe. [If] he intended to say "second tithe" but he says "poor person's tithe," [or he intended to say] "poor person's tithe" but he says "first tithe," he has not said anything. [If he intended to say] "first tithe" and he said "second tithe," his words are permanent. Rabbi Yosei says, if he intended to separate poor person's tithe [but said "second tithe"], he has not said anything. If instead of "second" [he said] "first," his words are permanent.

A Gentile that [separates] terumah -- his terumah is valid terumah (but see Ter. 1:1). In what case does this apply? [In the case of] a threshing floor, he separated terumah and gave it to a Kohen, [or separated] first tithes and gave them to a Levite [or separated] poor person's tithes and gave them to a poor person. [If his] produce is properly tithed [but] he brings his produce into his house, his produce is [considered] spoiled. An Israelite who is suspected of having brought his produce into his house, his produce [is considered] spoiled. A Samaritan is like a Gentile, the words of Rebbi. Rabban Shimon ben Gamaliel says, a Samaritan is like an Israelite.