Source? Looked for Source! There is None that would implicate Iran in any way. Even somewhat the opposite:

According to Armenians themselves:

verbatim from Armenian historian https://en.m.wikipedia.org/wiki/Vartan_Gregorian
:

"""
Many Christians, and even Muslims who were adherents of the Ithna ashari form of Shicism (aka pro safavid iran) were carried into captivity during those years. [21] (by ottamans)

Simeon Tigranakertsi, contemporary source, wrote "no one can describe either through writing or through speech the difficulties of times.",[22] In 1586 one who tried to do just that, the scribe Arakel Sarkavag, attributed all the ill to the
of sin accumulated by those who received the wrath of the epidemic of death through the sword, and starvation was not the end, he wrote, because after that the wolves dug into the graves and ate the dead.

* These conditions, compounded by heavy taxation, resulted in the first wave of immigration of the Armenians from historical Armenia to Isfahan. According to Arakel Davrizhetsi, the contemporary historian, this first wave of immigration included both Armenian notables, other property owners, and peasants; they were:
Sarukhan beg and his brother Nazar Jalal beg and his cousins, Oghlan Keshish and Ghalabeg, Melik Sujum, Melik Pashik, Melik Haigazn, Melik Baben and the entire inhabitants of four Armenian villages emigrated to Persia, and asked for the Shah's pro- tection and settled in Isfahan.
At the time there were already individual Armenian merchants in Isfahan. One of these prominent merchants, Khwajah Nazar, had received a royal edict in 1586 granting him individual protection and freedom to trade widely within the realm of Safavid Persia [25].

Immigration from the war-torm borderlands of the Safavid empire to its secure interior was not confined to Armenians alone. It included Kurdish chieftains, such as Ghazi Kh&nand Hayat Beg Ulamayoghli, and various Georgian noblemen disaffected from the Ottoman camp. Others included poverty-stricken peasnats fleeing from the chro- nic wars, heavy taxation and religious persecution.26

The Armenian Catholicisate in Etchmiadzln, near Erevan, the center of the Armenian Apostolic Church, ini- tiated contacts with the new rule of Safavid Persia, shah cAbbas I (1587-1629). The Catholicisate, a bone of conten- tion between rival Catholicoses, heavily indebted and convinced that Shah CAbbas would surely attempt to regain territories lost as a result of the Ottoman-Persian treaty of 1590, established contact with Shah cAbbas. One of the Catholicoses, along with two Archibishops, went to Isfahan. They were well received by the shah who, motivated to
attract commercial and artisan classes to his realm and to forge an anti-Ottoman coalition of Shicite Muslim, Georgian and Armenian leaders of Transcaucasia in his
forthcoming campaigns against the Ottomans to recapture
the lost territories of Armenia, Georgia, Kurdistan, Azerbayjan and Tabriz, its center, encouraged and welcomed disaffected leaders and emigrees from the Ottoman empire. Sh&h cAbbas accepted various Armenians into his service and according to Sherley was impressed with their competence and abilities.28

Further:

Shah Abbas also demonstrated a friendly diplomacy on the personal front.
In an effort to win the affection of his new sugjects and to demonstrate to others the esteem in which he held these Armenians, he paid periodic visits to the homes of such notables of New Julfa as Khw&jah Safar, Khwajah Nazar, and their children, Malikagha, Sultanum and Sarfraz. He encouraged his ministers to follow his example. He even attended church services on the occasions of Easter and Christmas. In addition, the shah gave the kalantar of New Julfa one of his royal seals. This was particularly use-
ful as a means of facilitating travel, bypassing otherwise necessary red-tape, and especially in making transactions and guaranteeing them with the shah's own seal.

According to Armenian tradition, in cases of disputes pitting his Christian Armenian subjects against his Muslim ones, the shah sided most of the time with his new subjects. In thus siding with the Armenians, the shah would stress that they had left their fatherland, their riches and their homes, and had come to Persia; therefore, trivial disputes should not obscure the fact that they were valued guests. Furthermore it had cost the king one thousand Tumans to bring each Armenian to Isfahan. All these sacrifices, the shah used to say, he had done not in the interest of the Armenians but for that of Persia. Such was the freedom of Armenians enjoyed that when in the bazaar disputes arose between a Muslim and an Armenian, the Armenian had the equal right with the Muslim to curse and cuss in kind, without fear of retribution.50
"""

sounds true about Ottomans. Wonder what was their point though.

You might already know better, but looks like short story is it was war zone. they looked towards the persian king for protection, moved to persia, 15 years later scorched earth policy was carried out, to keep the ottaman army out, Which worked. Shortly before this Armenians were told to move to iran. And the king did right by them.

Quick google scholar search explicitly for deportation didn’t help. I did find citation free red template wikipedia pages with titles such as forced deportation of armenians to iran, seemingly waiting for biased history to be inserted.

Also trivia they can have wine at home Today in Iran, whereas those of a muslim family can’t.

Reference:
Vartan Gregorian, Minorities of Isfahan: The Armenian Community of Isfahan 1587-1722, Iranian Studies, Vol. 7, 1974