Eruvin 37B

אלא אי בלקיחת בעלים, אי בעשיית כהן.

when they are purchased by their owner, if the owner explicitly consecrated it as a burnt-offering or sin-offering when he purchased it, or through the actions of the priest when he offers the birds as sacrifices. Therefore, even if the women did not verbalize their intentions, it is considered as if they had made a stipulation from the outset. Therefore, this case is not an instance of retroactive designation.

ואכתי: סבר רבי יוסי אין ברירה? והתניא: עם הארץ שאמר לחבר ״קח לי אגודה אחת של ירק או גלוסקא אחת״⁠ — אינו צריך לעשר, דברי רבי יוסי.

And still the question may be raised: Does R' Yosei really hold that there is no retroactive designation? Wasn’t it taught in a baraita: If an am ha’aretz, who is not known to be scrupulous in separating tithes, said to a ḥaver, one known to be meticulous in his observance of halakha and especially the laws of teruma and tithes, before the ḥaver went to the market to buy himself vegetables from another am ha’aretz: Buy for me as well a bundle of vegetables or a cake [geluska], the ḥaver does not need to tithe the food that he gives to the am ha’aretz. The only reason the food needs to be tithed is because it is demai, and an am ha’aretz is not particular about that issue. This is the statement of R' Yosei. It can be deduced from this ruling that R' Yosei accepts the principle of retroactive designation, as the ḥaver purchased bundles of vegetables without specifying which was for himself and which was for the am ha’aretz, and when he gave one to the am ha’aretz, it became retroactively clear that he had purchased that bundle for the am ha’aretz from the start, and therefore he does not need to separate tithes from it as demai.