This is not only the Presbyterian understanding but even some Reformed Baptists' understanding. I think Richard Barcellos was right in observing that many Reformed Baptists assumed a Covenant Theology like their Presbyterian brethren, while not looking at the distinct Covenant Theology of our Baptist forefathers. In a recent Reformed Baptist book, this idea was promoted:
It is absolutely imperative to understand that while there is just one Covenant of Grace, there are different methods of administrating it; each being of gracious promise serving the first manifestation of the Covenant of Grace (Genesis 3:15), culminating in the New Covenant, and enjoyed in eternal glory. This is not a flattening of Scripture nor is it “a reductionism which has the tendency of fitting Scripture into our theological system rather than the other way around.” On the contrary, the one Covenant of Grace exponentially builds, increases, and heightens throughout redemptive history until it crescendos in heaven.
Other Reformed Baptists contend that this view of "a single covenant, multiple administrations" is not the view of the signers of the 1689 Confession, but the Westminster Confession. There is a lot of similarity between the two Confessions, therefore, it is not strange for some Reformed Baptists to believe that our Confession (whether they've compared the two chapters or not, I do not know) must probably say the same thing as the Westminster Confession minus infant baptism. Therefore, they still operate according to the "one covenant, multiple administrations" model of Covenant Theology and not what we will now discuss, which we believe is the actual view of the Particular Baptists in the 17th century, but more importantly, a more biblical view.
Works like Pascal Denault's have raised doubts about the idea that our Baptist forefathers shared the same idea of administration in Covenant Theology with our Presbyterian brethren. In his work, Denault argues that for what has come to be known as 1689 Federalism. He goes back to the sources from the 17th century, the same period when the 1689 (which was actually written in 1677), the Savoy Declaration of Faith (1658) and the Westminster (1646) were written to see what the framers of the confessions actually believed. It appears from his research that many Baptists did not actually share the same understanding of Covenant Theology with their Paedobaptist brethren. There were some who did share Presbyterian covenantal view, no doubt. 1689 Federalism teaches that the Confession is not teaching the “one covenant, different administrations” model of Covenant Theology of Paedobaptists. But as it is obvious from the Westminster that it does teach the “one covenant, different administrations” (by their admission, see Westmins...