All perfect praise be to The Lord of The Worlds, and may His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
Zakah is a prescribed right due on wealth with conditions. It should be given to the eight categories stated in the following verse: "Alms are for the poor and the needy, and those employed to administer the (funds); for those whose hearts have been (recently) reconciled (to Truth); for those in bondage and in debt; in the cause of God; and for the wayfarer: (thus is it) ordained by God, and God is full of knowledge and wisdom." {At-Tawbah/60}.
There is no harm in paying Zakah on certain occasions provided that it is paid on its due time; however, it is permissible to pay it in advance.
Al-Imam an-Nawawi {May Allah be pleased with him} said: " Zakah is due immediately on the giver so long as both the money and the eligible recipients are present." {Al-Minhajj}.
In conclusion, if your (Asker) aunts and other relatives are poor, it is permissible to give them Zakah in the form of gifts on the Eid day. What counts is intending these gifts as Zakah without disclosing that intention to the recipients. Moreover, it is imperative that the giver makes that intention upon giving these gifts. As regards gifts of previous Eids, they can`t be considered as Zakah because the giver didn`t intend them as such when he first gave them. And Allah knows best.