I am trying to resolve what appears to be a conflict in several sources.
איזו סייג שעשה משה לדבריו?
הרי הוא אומר: (שמות יט) "ויאמר ה' אל משה, לך אל העם וקדשתם היום ומחר". לא רצה משה הצדיק לומר להם לישראל כדרך שאמר לו הקדוש ברוך הוא, אלא כך אמר להם: "היו נכונים לשלשת ימים אל תגשו אל אישה", והוסיף להם משה יום אחד מעצמו
What type of "fence" (precaution to prevent a violation of a mitzvah) did Moses do for G-d's commandment?
Behold it says (Exodus 19:10) "G-d said to Moses, go to the people and sanctify them today and tomorrow." But Moses did not want to tell B'nai Yisra'el exactly what G-d told them, but instead, he said to them (Ex. 19:15) "Be ready for three days; Don't touch a woman," and he added an extra day on his own.
In summary, the commandment G-d told Moses was to be ready for the 3rd day, meaning that they were to prepare for 2 days, and the Torah would be given on the 3rd day.
Moses says, to be ready (prepare yourself) for 3 days, meaning that the Torah would be given on the 4th day.
Yet, we see then when the "sound and light show" occurred, Exodus 19:16 (Sefaria) says:
וַיְהִי֩ בַיּ֨וֹם הַשְּׁלִישִׁ֜י בִּֽהְיֹ֣ת הַבֹּ֗קֶר וַיְהִי֩ קֹלֹ֨ת וּבְרָקִ֜ים וְעָנָ֤ן כָּבֵד֙ עַל־הָהָ֔ר וְקֹ֥ל שֹׁפָ֖ר חָזָ֣ק מְאֹ֑ד וַיֶּחֱרַ֥ד כָּל־הָעָ֖ם אֲשֶׁ֥ר בַּֽמַּחֲנֶֽה׃
And it came to pass on the third day, when it was morning, that there were thunders and lightnings and a thick cloud upon the mount, and the voice of a horn exceeding loud; and all the people that were in the camp trembled.
It says that this happened on the 3rd day, itself! So, how does Avot D'Rav Natan deduce that Moses added an extra day, since it seems that the event should have occurred on the 4th day, not the 3rd.