A rule of thumb is about 10 minutes per inch when frying it.. Fry one side 5 minutes, flip it over, fry another 5 minutes, test for flaking and when it does easily, it is finished.
when salmon(or any fish) flakes easily, it is done. Longer cooking makes it tougher, not more tender.
I buy small fillets of frozen salmon, which I thaw before frying in enough EVOO to coat the bottom of the pan. I fry the fillets for 6 minutes skin side down and 2 minutes on the other.