This work shows a study of the effect of the non-uniformity of photocathode response on the energy resolution of plastic scintillators optimized for pulse-shape discrimination. The studies were performed with Hamamatsu R7600U-200 and R9779 photomultiplier tubes. The pulse-height and pulse-shape spectra were obtained for a small piece of radon-222 loaded plastic scintillator positioned at different places on the photocathode. We show that alpha spectra can be approximated well with a normal distribution if the non-uniformity of the photon response of the photocathode is minimized. In the cases when the non-uniformity cannot be minimized, we propose an analytical function which describes the shape of the alpha peaks well under a variety of conditions. A possible effect of the non-uniformity of the photocathode response on the primary activity measurements by liquid scintillation counting is highlighted.