Mishna, Brakhot 2a: When the kohanim enter...where?

Question

Mishna, Brakhot 2a

מאימתי קורין את שמע בערבין משעה שהכהנים נכנסים לאכול בתרומתן

What is the author implying as the direct object of the verb נכנסים? In other words, from the hour that the kohanim enter...where?

Answer 1

The Tiferes Yisroel suggests that the mikvaos were outside the town (to avoid problems of mayim sheuvim). The Kohanim went to mikvah near to sunset to avoid having to be careful about their ritual purity during the day and so after their teviloh and drying themselves they did not come into town until it was dark.

So he understands that that the kohanim enter...town.

Answer 2

It implies 'begin' (as in time) as we find the same expression by other things Meshenichnas Adar. Here it means from the time that the Kohain - who was Tomey and concluded his Haerev Shemesh - may begin eating Terumah