They do not, self executing treaties become domestic laws, if these laws are not constitutional then the treaty is pretty much void.

And non self executing treaties are meaningless they pretty much mean that the US government promised something but it is not compelled to do anything about it and there is no mechanism that would require it to comply.

The US constitution is supreme it takes precedence over anything the legislative branch might legislate and any action the executive branch might take.

Alien tort is also not accepted when interpreting the constitution so you literally cannot interpret the constitution from the point of view of international or foreign laws.