Thanks for uploading the images. I get the same result from StarGenerator on all supported platforms, so there's no longer a bug in the Windows version of this tool —this is good stuff!
Indeed there are differences in the star positions between your real image and the StarGenerator synthetic image. On one hand, the differences in the four corners of the image are obviously due to field distortion (field curvature, I guess). The other differences are probably due to small accumulated errors in the computed proper motions. Although the PPMX catalog is very accurate, bear in mind that some of the proper motions have been calculated from astrometric observations gathered during very long periods.
As a counter-test, I have generated two versions of the StarGenerator image: one for your observation epoch (2010/05) and another for the J2000 epoch. When I register both synthetic images with your real image, StarAlignment computes consistent inlier quality factors of 0.5 and 0.4, respectively. In other words, when the correct epoch is specified in StarGenerator, StarAlignment can find more star pair matches between the generated synthetic image and your real image. This clearly shows that applying proper motion corrections improves the result. However, as I've said this isn't perfect.
In my tests, selecting the 2-D surface spline interpolation algorithm in StarAlignment provides somewhat better results, as this algorithm can correct small-scale distortions better than the default homographic projection. However this doesn't fix the problem completely.
Having said that, I think you should have no problems to build your mosaic on top of a synthetic StarGenerator image. Although not all of the stars will match, StarAlignment will be able to find a valid transformation for your four mosaic frames.