A faulty brine valve assembly or damaged rotor valve can cause the salt tank to overflow.
The brine valve assembly should shut off water flowing into the salt tank when brine water reaches the correct level. Replace the brine valve assembly if it doesn't shut off fill water causing brine water to overflow the tank.
A damaged rotor valve can leak water into the salt tank causing water to overflow the tank. Check the rotor valve for damage and replace the rotor valve if it leaks water into the salt tank.
These repairs may help solve your water softener problem
Replace the water softener brine valve assembly
The brine valve assembly inside the brine well controls the brine water level. The brine well won't fill properly if the brine valve assembly is damaged. Replace the brine valve assembly if it's broken or damaged.
Replace the water softener rotor valve
The rotor valve directs water through the water softener to complete functions such as softening water and flushing the resin filter. A defective valve leaks water or locks up and doesn't move. Replace the rotor valve if it leaks or it's damaged.