יֵשׁ בְּמַעֲשֵׂר וּבִכּוּרִים מַה שֶּׁאֵין כֵּן בַּתְּרוּמָה, שֶׁהַמַּעֲשֵׂר וְהַבִּכּוּרִים טְעוּנִים הֲבָאַת מָקוֹם, וּטְעוּנִים וִדּוּי, וַאֲסוּרִין לָאוֹנֵן. רַבִּי שִׁמְעוֹן מַתִּיר. וְחַיָּבִין בַּבִּעוּר. וְרַבִּי שִׁמְעוֹן פּוֹטֵר. וַאֲסוּרִין כָּל שֶׁהֵן מִלֶּאֱכֹל בִּירוּשָׁלַיִם. וְגִדּוּלֵיהֶן אֲסוּרִים מִלֶּאֱכֹל בִּירוּשָׁלַיִם אַף לְזָרִים וְלַבְּהֵמָה. רַבִּי שִׁמְעוֹן מַתִּיר. הֲרֵי אֵלּוּ בַּמַּעֲשֵׂר וּבַבִּכּוּרִים, מַה שֶּׁאֵין כֵּן בַּתְּרוּמָה:
Ma'aser and Bikkurim share [laws] that are lacking in Terumah: that Ma'aser and Bikkurim must be brought to a [specific] place, require verbal recitation, and are prohibited to an Onen [a person whose close relative has died but has not yet been buried], while Rabbi Shimon permits. They both require removal [from one's home], while Rabbi Shimon exempts. Any amount of them [when mixed with normal food] is prohibited to eaten in Jerusalem. Any growth that comes from them may not be eaten in Jerusalem, neither by a non-Kohen, nor an animal, while Rabbi Shimon permits. All of the above is for Ma’aser and Bikkurim, but not for Terumah.
The Bartenura on R’ Shimon’s lenient rulings on Onen and removal limits it to Bikkurim. By Ma’aser, everyone agrees that the verses in the section of Vidui Ma’aser apply, including לא אכלתי באני - “I did not eat it as an Onen” - and the preceding several verses regarding destroying said Ma’aser. However, Bikkurim is called Terumah, and therefore, just as Terumah is exempt from these laws, so, too, Bikkurim.
TLDR: According to everyone, Terumah is exempt from the laws of Onen and destruction, learned out from the verses in Vidui Ma’aser.
Now compare to Ma’aser Sheini 5:10:
בַּמִּנְחָה בְיוֹם טוֹב הָאַחֲרוֹן הָיוּ מִתְוַדִּין. כֵּיצַד הָיָה הַוִּדּוּי, בִּעַרְתִּי הַקֹּדֶשׁ מִן הַבַּיִת (דברים כו), זֶה מַעֲשֵׂר שֵׁנִי וְנֶטַע רְבָעִי. נְתַתִּיו לַלֵּוִי, זֶה מַעְשַׂר לֵוִי. וְגַם נְתַתִּיו, זוֹ תְּרוּמָה וּתְרוּמַת מַעֲשֵׂר. לַגֵּר לַיָּתוֹם וְלָאַלְמָנָה, זֶה מַעֲשַׂר עָנִי, הַלֶּקֶט וְהַשִּׁכְחָה וְהַפֵּאָה, אַף עַל פִּי שֶׁאֵינָן מְעַכְּבִין אֶת הַוִּדּוּי. מִן הַבַּיִת, זוֹ חַלָּה:
By the afternoon of the last festival day, they would make the declaration. How was the declaration made? "I have removed the Kodesh [consecrated material] from the house" (Deuteronomy 26:13)--this is Ma'aser Sheni and Neta Revai. "Have given them unto the Levite"--this is Ma'aser Levi [The first tithe of produce, which must be given to the Levi]. "And also I have given it"--this is Terumah and Terumat Ma'aser. "And also to the stranger, to the orphan, and to the widow"--this is the poor man's tithe, Leket [fallen gleanings given to the poor], Shikhecha [forgotten gleanings given to the poor], and Pe'ah [corner of a field given to the poor], even though these do not invalidate the confession [if they have not been given]. "From the house"--this is Challah [dough that must be set aside for the priest].
Emphasis is mine.
If Terumah is included in Vidui Ma’aser, it stands to reason that the laws of Onen and destruction, learned from said passage, should apply to Terumah as well, and if so, Bikkurim should also be included.
Are we forced to say that there is a machlokes Tannaim, and according to the Tanna in Ma’aser Sheini, Terumah is indeed included in those laws? If so, how do the Tannaim in Bikkurim learn the passuk expounded in Ma’aser Sheini to include Terumah?
All quotes come from Sefaria.