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When speaking of the primacy of the universal church to the local church this concerns their historical and ontological relationship; it does not address their relationship once the local church is established. Primacy in this sense does not establish supremacy. Cardinal Kasper argues for a spontaneous foundations of local churches from which the universal flows because of their union in faith.

Many exegetes are convinced that the "Pentecostal event" in the Acts of the Apostles is a construction by Luke. Similar "Pentecostal events" also occurred, probably from the beginning, in the communities of Galilee.

This he contrasts to the traditional understanding of a single "Pentecostal event" in which the universal church was established and from which the local churches flowed. Thus Cardinal Dulles writes:

Unlike the state, the church was established from above, so to speak, by God’s action in Christ, who gave special powers to Peter and the Twelve. The church began to pulse with life when the Holy Spirit descended upon the church as a whole at Pentecost. Only subsequently, as the faith spread to Antioch, Rome, Alexandria and other cities, was it necessary to set up local authorities in charge of particular churches. The particular churches were, as Vatican II puts it, "fashioned after the model of the universal church," which is therefore antecedent to them, even though it in certain respects depends on them ("Dogmatic Constitution on the Church," No. 23).

But as I have stated, this does not address directly the relationship between the universal church and the local church one the latter is established. Is this the statement of Cardinal Dulles to which you are objecting?