You will pull from the brine tank until all the water is sucked out and a check valve stops the flow. It's a brine fill/slow rinse process, so after all the brine is drawn out, it continues to push plain water slowly thru the resin.
I'm curious why you chose 40mins/5gals for your brine fill? (5 gals at 3 lbs per gallon = 15 lbs total, / 2 cu ft) That's 7.5 lbs of salt per cu ft, not exactly a common number I have seen before. 4, 6, 8, 10, and 15 seem to be more common. I'd estimate 7.5 lbs will get you about 46K worth of capacity, but some of the pros may know the exact amount better than I, a simple home owner like you.
If it were me, and you have no iron in your water, I'd go with 6 lbs per cu ft. That's 12 lbs per regen. In order to get that, use 0.125 X 32 = 4 gallons, as each gallon dissolves about 3 lbs of salt. 6 lbs is pretty efficient, and it should serve you fairly well. Assuming 60 GPPPD for 3 people, you will consume about 438 lbs of salt per year, and regen every 10-11 days or so (more or less, based on actual water usage).
Hope this helps, and if anyone sees an error in my suggestion, feel free to correct me!