With a water softener that is operating properly, the water should not taste salty. The salt should be totally rinsed from the system during the brine and rinse cycle of the regeneration process, except for the sodium which exchanges onto the water softener's resin replacing calcium and magnesium. During the service cycle, hardness in the water is exchanged for sodium.

If your water tastes salty, it is likely that the water softener is malfunctioning, such as a stuck valve or valve that isn't seated properly. You could try cleaning the venturi valve and directions for doing this are in your owner's manual. Otherwise, you should call a reputable water dealer to have the unit checked.