We apply to the specific case of images taken with the ROSAT PSPC detector our wavelet-based X-ray source detection algorithm presented in a companion paper. Such images are characterized by the presence of detector ``ribs'', strongly varying PSF, and vignetting, so that their analysis provides a challenge for any detection algorithm. First, we apply the algorithm to simulated images of a flat background, as seen with the PSPC, in order to calibrate the number of spurious detections as a function of significance threshold, and to ascertain that the spatial distribution of spurious detections is uniform, i.e. unaffected by the ribs; this goal was achieved using the exposure map in the detection procedure. Then, we analyze simulations of PSPC images with a realistic number of point sources; the results are used to determine the efficiency of source detection, and the accuracy of output quantities such as source count rate, size and position, upon a comparison with input source data. It turns out that sources with 10 photons or less may be confidently detected near the image center in medium-length (about 10000 sec), background-limited PSPC exposures. The positions of sources detected near the image center (off-axis angles less than 15') are accurate to within a few arcsec. Output count rates and sizes are in agreement with the input quantities, within a factor of two in 90% of cases. The errors on position, count rate and size increase with off-axis angle, and for detections of lower significance. We have also checked that the upper limits computed with our method are consistent with the count rates of undetected input sources. Finally, we have tested the algorithm applying it on various actual PSPC images, among the most challenging for automated detection procedures (crowded fields, extended sources, nonuniform diffuse emission). The performance of our method in these images is satisfactory, and outperforms those of other current X-ray detection techniques, such as those employed to produce the MPE and WGA catalogs of PSPC sources, in terms of both detection reliability and efficiency. We have also investigated the theoretical limit for point-source detection, with the result that even sources with only 2-3 photons may be reliably detected using an efficient method in images with sufficiently high resolution and low background.