Just look at the numbers of problem sent by MW2121
After complete hydrolysis of ASA you can expect concentrations of sodium salicylate and sodium acetate between 0.01 to 0.02 M.
What may be the pH of these salts present in the solution individually? My guess - below 8 and about 8.5, respectively. You can check by calculations).
When these salts are taken together in solution and additionally Na+ ions in the solution will be in excess (from NaOH or later NaCl), then hydrolysis will take place to a lesser extent and we can expect pH of this solution slightly below 8. The color change of phenolphthalein is above 8.2, so in titration, these salts will not participate. And that's what we want.