A group of us Israelis (formerly Canadians) met last year in Canada for Sukkos. We decided to form a minyan on Isru Chag (which was Simchas Torah there). Most of us brought our Tefillin to Shacharis. One fellow protested that we were forbidden to don Tefillin as the predominant practice was Yom Tov.
What does the Rabbi say?
Thank you for your question. I have some hard news for you – even though your intentions were for the sake of heaven – I believe it was improper for you to even form a separate "Israeli" weekday minyan on second day Yom Tov outside Israel. Before we examine your question about tefillin, we need to examine how an Israeli should act on second day Yom Tov when visiting Chutz La'Aretz.
If an Israeli finds themselves in a Jewish community outside Israel on second day Yom Tov, they are not allowed to do any melacha (forbidden Yom Tov labours) (Shulchn Aruch, Orach Haim, 496,3). This is true both in public and in private (Mishna Brurah, ibid, 9). The reason for this is to make certain that there will be no arguments between the visiting Israelis and the local community, or belittling of the holiness of the second day festival.
However, an Israeli in such a situation is obligated to pray the weekday service, as for them it is not Yom Tov. This too must be done in such a way as not to cause any arguments or belittling of the local community. Thus we arrive at the question of whether a separate Israeli weekday minyan is allowed. The halacha is that such a minyan is forbidden – (See Yom Tov Sheni Be'Halacha, chapter 3,26). This view is held by all major Rabbis (Rav S.Z. Aurbach zt"l, Rav Elyasiv zt"l, Rav Z.P. Frank zt"l, Rav Aba Shaul zt"l, and many others). This is true even if the minyan is held in a completely separate location that the local community does not know about.
So, after we have established that the Israeli minyan was a mistake (… not to feel too bad… if only all our sins were because we wanted to daven in a minyan!...) what should you have done?
You should have put tefillin on at home, privately, and prayed by yourselves. Then, if you so desired, you could have walked to synagogue to hear kaddish, kedusha etc. Other Rabbis say you should have put tefillin on at home, privately, and just said Shema, and then take them off and go to synagogue to pray (weekday prayers) with the congregation (who would be saying Yom Tov prayers). If your presence in synagogue is going to be noticeably missed, you should certainly follow the second practice (See Igrot Moshe, Orach Haim, 3, 72).
May you be blessed that the holiness of Eretz Yisrael accompany you in all your deeds.