Apart from the Italo-Byzantines in the Kingdom of Naples, the Chaldean Church of Mesopotamia, and the Maronites of Lebanon, no Eastern Churches were in communion with the Papacy in 1570. Quo Primum has no authority over Eastern Churches, nor could it as it was intended for the Latin Church sui juris. The Ukrainians restored communion with Rome soon after the Council of Trent. Their treaty of union (Brest) is very explicit that they entered into communion with the Bishop of Rome whilst retaining their faith, worship, discipline, and hierarchy as Orthodox Christians.

Although there are a minority of Easterner Catholics directly under the Holy See because their Churches lack Patriarchs or Major Archbishops and, thus, are not Churches sui juris (even thoughf their Orthodox or Nestorian analogs may in fact be Churches sui juris because they enjoy autocephaly), Eastern Catholics ARE NOT UNDER the Pope. They are IN COMMUNION with the Pope, but remain equal, autonomous, self-governing Churches. Key here: Communion with, not subordinate to the Papacy!

The power and authority of the Petrine Office is not unlimited, but circuмscribed by the definitions of Pastor Æternus of Vatican I on the Primacy and, more so, the very Status Ecclesiæ (unwritten constitution of the Church) itself. Ultramontanism is as much error by excess as conciliarism and Gallicanism are errors by defect.

Quo Primum is addressed to the Latin Church ONLY! It is not an exercise of the universal ordinary or extraordinary Papal Magisterium. It belongs only to the everyday disciplinary papal administration of the Roman Church.