That parasite shouldn't be that quick to kill a fish without any signs of white spots on any of the fishes... Did you notice any white spots on them before?
Cause of ich is by due to quick temperature fluctuations, which causes stress to the fishes and causes the weakening of the immune system in the fishes... They are an opportunistic parasite, present in the aquarium, and they wait for when the fishes are stress and their immune systems are compromised (at least, that's what I think causes the parasite to thrive)...
The salt treatment should be effective against ich due to a difference in salt concentration in the water (tank water + salt) and the concentration in the parasite (protozoan). Due to the difference in salt concentration, the water in the parasite will be expelled in an attempt to equalize the concentration in the environment and in the cell.
If the fishes would be able to handle it (tropical fishes), I would raise the temperature to 86F... I think you could even go to 90F. A higher temperature would quicken the life cycle of the parasite and therefore, would go to the form which would be more vulnerable towards the salt. A temperature of 82F would take longer to treat a tank with ick, than in a higher tank temperature.