In the comics, Tyrone and Tandy were among the many runaways who were swooped down and preyed upon by minions of drug kingpins who needed human test subjects. They were trying to design a drug themselves in order to control the flow of it, and avoid exorbitant import costs. The experiment failed, and all of the subjects died, except for Tyrone and Tandy. (At one point, they were thought to be mutants, and the experiments unleashed their latent powers, but that was retconned later.) In their very first appearance, they were seen to be taking revenge against the drug lords who accidentally created them.
About the only aspect of their origin that the show keeps is the presence of water. In the comics, the experiments were being held on Ellis Island (which, when the comic was written in 1983, was closed to the public), and they escaped by swimming in the Hudson River. On the show, they get their powers much younger, as little kids. Tyrone dives into the Gulf of Mexico after Billy is shot and falls in, and Nathan Bowen is driving his daughter home when his car crashes into the river. An accident on a Roxxon oil rig (still unexplained as of episode three) seems to be the catalyst for Tandy and Tyrone’s link and their light-and-dark powers. But those powers don’t manifest until years later.