A softener should have a minimal affect of the tase of water. If you are getting a truly salty taste to the water, it should only occur after a regeneration if there is a problem with the softener and should clear up after running the water for a short amount of time. if you get salty water in the water heater, it will take considerably longer to get that cleared due to dilution issues. If your system produces salty water, you have a problem. Extended salty taste out of a softener would usually indicate a bad or missing riser o-ring, or a short manifold assembly.
We need more information to help you. A picture of the unit, water source (well or municipla), how old the unit is etc.
Hope this helps!