Irving seems to be a rainbow trout (Oncorhynchus mykiss), a species of freshwater salmon native to cold-water tributaries of the Pacific Ocean in Asia and North America. They're a sea-run form of the coastal rainbow trout (O. m. irideus) that usually return to fresh water to spawn after living two to three years in the ocean. Freshwater forms known as steelhead trout have been introduced into the Great Lakes and often migrate into tributaries to spawn.
Trout are a freshwater fish. They live in streams, rivers and lakes. It would be impossible for Irving to cross the ocean and live in the Castaway's lagoon.