When the water softener goes through a regeneration it puts brine water into the resin bed to clean it. If water is used in the home during the regeneration salty water can be drawn into the house plumbing.
Check the regeneration time and the time of day setting on the softener. Water softeners are set to regenerate at 2:00 AM because most households are quiet at this time. Regeneration takes around 1 1/2 hours. If this is a bad time for you, you can change the regeneration time.
The owners manual shows how to do this and also to set the time of day. You can download, view, or print a copy of the owners manual free at [managemylife.com
Another possibility is the brine rinse or the fast rinse is not working. You can run the softener through a "regenerate now" cycle and check the rinses. At the end of the second rinse the water going down the drain should not taste salty.