The Outer Continental Shelf Lands Act, usually called OCSLA, is the federal statute that sets the ground rules for structures far offshore. The outer Continental Shelf is the submerged land beyond state waters that falls under federal control.
If you were hurt on a structure out there, 43 U.S.C. § 1333(a) is what places you inside federal law. It extends the Constitution, laws and civil and political jurisdiction of the United States, "to the same extent as if the outer Continental Shelf were an area of exclusive Federal jurisdiction located within a State," to the subsoil and seabed of the outer Continental Shelf; all artificial islands on it; installations and other devices permanently or temporarily attached to the seabed for exploring for, developing or producing resources, including non-mineral energy resources; and any such installation or device, other than a ship or vessel, used to transport or transmit those resources.
The statute also borrows the law of the nearby State, in a specific way. To the extent they are applicable and not inconsistent with OCSLA or with other federal laws and regulations, the civil and criminal laws of each adjacent State are declared to be the law of the United States for the area that would be within that State if its boundaries were extended seaward to the outer edge of the outer Continental Shelf. Federal officers and courts administer and enforce those laws, and the statute says this adoption gives no State any claim of jurisdiction over that area.
For an injured worker, this means a fixed platform on the outer Continental Shelf generally sits in a federal legal framework, not a purely state one. Some state rules may shape a claim, but only as borrowed federal law, only where they fit and do not conflict with federal law, and in federal courts. Whether a given adjacent State's law is borrowed, and which parts of it fit, are questions the facts decide. Where the platform sat relative to the outer Continental Shelf is the starting point for the statute's reach, and it is one of the things an attorney conversation can help sort out.