If you add softened water to a swimming pool with hard water rather than draining and refilling how could the addition of soft water be corrosive?

The corrosive properties of water are not affected by its hardness. This is a common misconception that can be explained by the types of source water that yield naturally soft or naturally hard water. If your water is naturally soft, there is a good chance it is also corrosive due to other factors.

Surface water sources that supply naturally soft water often have low (acidic) pH, low TDS (total dissolved solids), and high dissolved gas concentrations such as oxygen and CO2 that can contribute to corrosion. Naturally hard water often comes from a well and has higher pH, higher TDS, and lower dissolved gas concentrations. These correlations are due to the water source and are not caused by the hardness of the water.

If your water has been softened using sodium cycle ion exchange in a water softener, the corrosive properties of your water are not affected. A water softener removes calcium and magnesium ions and replaces them with an equivalent amount of sodium ions. This process has no significant effect on the corrosive properties of the treated water.

Removing hardness by reverse osmosis (RO) or deionization (DI) can significantly increase the corrosive properties of water because they both drastically decrease the dissolved solids in the water, and the latter can alter the pH. This sort of filtration is beyond the scope of the question.

You still must maintain the correct pH and alkalinity levels in your pool, though your water softener will not affect these levels. Your local pool supply store can furnish you with the proper test kits and chemicals to accomplish this.