ויקרא פרק כב, ז וּבָא הַשֶּמֶּשׁ וְטָהֵר וְאַחַר יֹּאכַל מִן -הַקֳּדָשִׁים כִי לַחְמוֹ הוּא:
מסכת ברכות דף ב/א וממאי דהאי ובא השמש ביאת השמש והאי וטהר טהר יומא דילמא ביאת אורו הוא ומאי וטהר טהר גברא אמר רבה בר רב שילא א"כ לימא קרא ויטהר
A person that is tamei, may eat terumah the night after going to the mikveh and does not have to wait until bringing the korbanos the next day. Thus, the verse is explained ובא השמש וטהר that when the day passes, one becomes tahor without any other action and it does not mean that after the new arrival of the sun (sunrise) and then another action would be required prior to being tahor (bringing one’s korbanos). If the verse had meant the latter, then would have written ויטהר a language of future tense. Rather, the verse wrote וטהר in the past tense that was not tahor and now becomes tahor by itself without waiting for another action.
In regards to terumah outside of Eretz Yisrael and Chalah nowadays (which is also called terumah), both considered obligated from the rabbis to give to a Cohen. Some poskim state a Cohen still needs nightfall prior to eating. But the majority of poskim say a Cohen can eat these items right after going to the mikveh. The Rema brings that one may bake matzah on Yom Tov in order to give it to a Cohen who may eat the Chalah portion. (This is not a halachic ruling)
