Standard Oil's refinery isn't on the former Naval base. It's on the right hand side of the highway, as you head from the Naval Base towards Makaha.
When I was in Hawaii, the base was still active. Had a pass to get on and play golf. I suspect the now Tesoro refinery was built on the naval base with the lease term that all production required would first go to the naval base, ships, airplanes, naval base cars. I suspect those industries kept that refinery busy.
Honolulu has a population of about 1 million, or a bit less. The entire state has another 300,000 people, so that's 1.3 million people total for the state.
Not a big market, but, the shipping and airline industries, not to mention the U.S. Military ships speak for themselves.