The new water is less dense than your pool water, so it floats on top and pushes the salty, colder water down.
The ticket is to keep the water still. Be sure to shut off anything that could mix water. A random start of the pool pump in the middle of it would wreck it, or anything like a water feature, spa, etc. No brushing, no swimming, pool pump off, yada, yada. If it was real windy, you could put the cover on it if you had one, or wait for an average day.
If you can't match flow, just let it fill up high, then shut off your fill line for a bit, or vice versa. Measure the flow rate (how long to fill a 2-gallon pail) of your fill line and track the time in minutes X gallons per minute, and let it run the amount of time that equals the gallons you want to get rid of.
A call to your water supplier might be worthwhile. Rule out the chance that they're using your consumption to determine your sewer rate for the upcoming year. If need be, do it after the period they use for sewerage estimate. Ask if any fees or higher incremental rates are avoidable for a pool refill.
- - - Updated - - -
Whoops, should have checked, others had you covered.