This doesn't seem to be a case where the invading species gains an immediate upper hand in its new environment. (Cf., the rampant python population in the Florida Everglades.) In this case, the invading Atlantic species faces stiff and probably superior competition from the various Pacific salmon species, which are every bit as big and fast, and which fill the same ecological niche. Hell, a Pacific Chinook will get twice as big as an Atlantic salmon. It also knows the territory, including where and what to hunt, and its wild instincts haven't been dulled in a fish farm.
If I were a betting man, I'd wager on the native Pacific populations over the scattered pockets of farm-raised exotics nearly 99 times out of 100. Barring human involvement, of course. If we hunt the Pacific species out of existence, or damage the environment beyond recognition, all bets are off.