You probably mean the Hague Peace Conference held in July 1899. That was when "bullets that expand or flatten easily in the human body" were first proscribed. The United States was never a signatory to the Hague Peace Conference which meant that not only could the United States use those rounds but also that if the US entered a conflict all the other parties could use them too.
The United States did, however, sign the Hague Convention 1907, Article 23(e) which forbade: "...arms, projectiles, or material (sic) calculated to cause unnecessary suffering." As a result, US snipers used M-118 ammo, a "Match" version of M-80 ball. (7.62×51mm 173-grain solid-tipped boat tail).
In late 1985, the Judge Advocate General wrote an opinion which affirmed that expanding ammo was legal for the US to use in operations "not involving the engagement of the armed forces of another State" (like counter terrorist operations, for example).
In 1990, another opinion permitted the use of the Sierra MatchKing hollowpoint round by US snipers, reasoning that it was not designed to expand or fragment and that the hollowpoint design was a result of the requirements for manufacturing super-accurate bullets.
Then in 1993 Special Operations Command was given the go-ahead by the Judge Advocate General to equip their forces with JHP rounds (Winchester "Black Talon" at the time) for their H&K MK 23 pistols.