The brining cycle also includes a slow rinse cycle. A typical brine draw rate will be .25-.5gpm, depending on the capacity of the softener, so if your system has a .5 gallon per minute flow restrictor, at 12 minutes, that would be 18#'s of salt. The other 48 minutes is the slow rinse cycle. In the brine tank is a float assembly. Within in this float assembly is an "AIR CHECK". This is a small ball at the bottom of the float that seats when the water is depleted from the salt tank. When this ball "seats" in the float it prevents air from being drawn into the system.
The refill cycle time and height setting of float determines the amount of water needed to dissolve the proper amount of brine for regeneration.
IE: 12min refill @ .5gpm = 18lbs of salt (3lbs of salt per gallon of water).
This can be adjusted for higher efficiency depending on water chemistry and usage.