Salt does not kill white spot (Ichthyophirius). White spot is found in fresh, brackish and salt water aquariums.
Salt will kill some external parasites like Costia, Chilodonella and Trichodina.
-------------------
The parasites fall off the fish after a couple of days so even tho the fish don't have as many spots now, it doesn't mean they are free of the disease. It simply means the parasites have moved into the next stage of their lifecycle, where they divide inside their white spot cyst that is sitting on the bottom of the tank. In a couple of days the cyst will open and release hundreds of new parasites into the water.
-------------------
White spot can find fish in the dark, just like velvet parasites can. They pick up on chemicals, carbon dioxide and movement coming from the fish. And when you have thousands of parasites in the water, some of them are bound to come across a fish.
-------------------
You could try Praziquantel (tapeworm treatment for dogs, cats and fish). One of the shops I knew claimed they used Praziquantel on tanks with white spot and it cured the problem. I can't guarantee it will work because I didn't do treatment, but I do trust the people who did it.
Praziquantel is safe and won't harm the fish. It remains in the water for a few days so you would have to do a big water change after a couple of days and re-treat the tank.