Did you even read the section I named? It goes like this:
The clause that prohibits states from entering into treaties, alliances, and confederations without consent of Congress is 1.10.1. The one prohibiting the formation of new states by combining existing states is 4.3.1. 4.3.2 has nothing to do with that and everything to do with the authority of the United States over its territory.
With this same logic, a state in South America cannot enter into any alliance, treaty or confederatin without the approval of Congress.
Again, this is pertaining to states who are members of the UNION. For example, Texas, Oklahoma, and Louisiana (TODAY) cannot enter into a treaty, alliance, or confederation with one another, because they are part of the Union. This cannot happen with states in the UNion, because then you have problems withing the UNion, and rivalry among different Confederations, alliances, etc...within the nation.
In 1861, the states, not prohibited by the Constitution, seceded and no longer were subject to this law. Once they seceded, they were no longer states of the Union...therefore, this article does not apply. Since the Constitution did not forbid the secession, they seceded and were no longer subject to the laws of the U.S. They were not longer U.S. states in Confederation with another, they became a completely separated part of the landmass and were states of the Southern Confederation. You are on the premise that after the states secedeing, they were still part of the U.S., when in fact they weren't....because the Constitution did not prohibit secession, therefore, powers not prohibited to them, were reserved to them. And since secssion was not prohibted in the Constitution as of 1861, then the power was reserved to the states.