Normally salmon soup is made with salmon cut into 1cm to 2cm cubes or similar pieces. At that size immersed in simmering stock, it does indeed only take salmon about 5 minutes to cook fully (see Serious Eats recipe, which cooks it for 3 minutes). Try fishing a piece out after that time; you'll see that it's cooked through. If you're really concerned with the safety of the fish, you could go as high as 10 minutes. If you cook the fish a lot longer, though, the salmon will tend to disintegrate into tiny fragments, which probably isn't what you want in the soup.
Also, you don't want to boil the salmon; you want it to be cooking at a gentle simmer. If the pot is at a roiling boil, the salmon will probably come apart much faster and make for a cloudy, sludgey soup.
Pork and beef have a thick connective tissue which keeps them together, and takes a long time to gelatinize so that the meat will be tender. Fish does not have this kind of connective tissue, and for that reason cooks much faster.