Tosefta к Дмай 2:4

Certainly untithed produce that was tithed (lit., "fixed") as Demai (i.e., the owner thought it was Demai so he only took out Terumah of tithes (Dem. 2:4), per Minchat Yitzchak), or Demai that was tithed as certainly untithed produce (and thus took Terumah from the whole), he has done nothing (i.e., the tithe is not effective and the status remains as it was), the words of Rabbi Ya'akov (alt., "Rabbi Meir," per MS Erfurt). Rabbi Yosei says, [as to] certainly untithed produce that was tithed as Demai, nothing has happened, [but as to] Demai that was tithed as certainly untithed produce, its tithes are [considered valid] tithes, but its Terumah is not [valid] Terumah, as one may not separate Terumah after Terumah [has already been taken]. [Note: Since even an am ha'aretz is presumed to have separated Terumah, separating Terumah here would result in two Terumahs taken from the same produce (see Minchat Yitzchak here).]

As for olives, [their status for purposes of Demai] is determined from the time they are made into oil (משיעסום not משיחסום per GR"A), [depending on whether they are pressed] in the larger olive press or in the smaller olive press (see Sheviit 8:6 (בד/בודידה)), the words of Rabbi Meir. But the Sages say, neither [all] larger olive presses nor [all] smaller olive presses are comparable, either in the towns or in the provinces. The majority in the towns is not [like] the majority in the provinces; what is permitted [to buy, sell, or consume without tithing] in the towns is prohibited in the provinces (i.e., the majority of certain species of produce in the towns is generally imported and not subject to tithes, while the majority of that same species sold in the provinces is grown in the Land of Israel and thus treated as Demai, see Y. Dem. II.1.8, and Mishneh Torah, Tithes 13:12)). [Conversely,] the majority in the provinces is not like the majority in the towns; what is permitted in the provinces is prohibited in the towns. The majority in the mountains is not like the majority in the valleys; what is permitted in the mountains is prohibited in the valleys. [Conversely,] the majority in the valleys is not like the majority in the mountains; what is permitted in the valleys may be prohibited in the mountains. The majority [of produce sold by] the store-owner is not like the majority [sold by] the homeowner; what is permitted [to sell without tithing] for the storeowner is forbidden for the homeowner. [Conversely,] the majority [of produce sold by] the homeowner is not like the majority [sold by] the store-owner; what is permitted for the homeowner it forbidden for the store-owner. And this is the general rule: Whenever [foreign produce] forms the majority of it (i.e., of all produce of that species), it is permitted [to buy, sell, or consume without tithing], [and whenever foreign produce does] not form the majority of it, it is forbidden [to do so without tithing]. If [the foreign produce] formed the majority, and it diminished, the marketplace returns it to its former status (see Sanhedrin 19a:12 re "חזר...ליושנו"). Rabbi Yosei said, it so happened that a "threshing floor['s worth] of beans" entered Meron [from outside the Land of Israel], and they came and asked Rabbi Akiva, and he permitted them to [go to] the marketplace [to purchase the beans without tithing them as Demai, since the foreign beans formed the majority (see Minchat Yitzchak here)]. They [then] said to him, "Rabbi, it diminished" (i.e., the foreign beans are now the minority) and he said to them, "The marketplace has returned to its former status [and thus all produce must once again be treated as Demai]." Rabbi Shimon says, even if only a single "threshing floor" [of foreign produce] entered a city [and did not form a majority], the bakers are permitted [to sell it without first separating Demai (see Dem. 2:4)] because they "run after the new" (i.e., bakers only purchase new produce, so they need not measure new foreign produce against all domestic produce of that variety).