Why does adding a capacitor to the adjust pin of a voltage regulator improve PSRR?
That regulator senses voltages with respect to its output pin, it tries to keep its ADJ pin 1.2v below the output.

Consider what the output ripple means. It not only means the output ripples with respect to the ground. It also means the ground potential is rippling with respect to the output pin.

Without that capacitor, the ripple arrives at the regulator ADJ pin through the R2/R1 potential divider, so it only rejected with that low gain.

With Cadj, the ripple on the ground terminal arrives unattenuated at the ADJ pin, so there is much more loop gain available to reject it. Study the rejection graphs carefully. You'll find the difference with and without Cadj is equal to the R2/R1 attenuation ratio.