Until the Ben Eretz Yisroel reaches a Jewish settlement in Chutz o’Oretz, s/he has no obligation on Yom Tov Sheni to abstain from Meleches Avodah.
We did look at a Hebrew calendar and the ones in Israel don’t have a second day printed on it. More likely it had “Nosso” printed on it in conjunction with Shabbos Erev Shovu’os.