The Fair Labor Standards Act (FLSA), applies generally to employment within American Samoa as it does to employment within the United States. The minimum wage rates for American Samoa are set by a special industry committee (29 U.S.C. 205, 29 C.F.R. Part 511) appointed by the U.S. Department of Labor, as required by the Act. The rates are set for particular industries, not for an employee's particular occupation. The rates are minimum rates (29 U.S.C. 206(a)(3)); an employer may choose to pay an employee at a rate higher than the rate(s) for its industry.
"The Act contains a number of additional requirements, including the payment of premium rates to certain covered employees who work more than 40 hours in a workweek (29 U.S.C. 207), limitations on the employment of minors, and provisions relating to the Act's coverage and exceptions to and exemptions from some of the Act's general requirements."
The way I'm reading the info, American Samoa is exempted from all minimum wage laws, not just the one the house passed. The North Mariana Islands were included in the bill in an effort to shutter sweatshops on the islands.