If you haven’t done so, you will want to identify the nuclei with the IdentifyPrimAutomatic module, adjusting the settings for object size appropriate for your image. Then, in CorrectIllumination_Calculate, you will want to adjust the block size and the filter size. The objective is to achieve a version of the original image in which the spots are blurred away but the background fluorescence in the nuclei is smoothed but still present. In this way, once you subtract the correction function from the original, you are left with just the spots.
Since the size of the nuclei in your images is smaller than those in the speckles example, you will probably want to adjust the block and filter sizes downward, perhaps to half that of the values in the speckles example. There is no precise rule for the “correct” values, just trial-and-error until you get favorable results. I also suggest inserting the PauseCellProfiler module in the module so you can run the pipeline to the point where you are interested, and halt execution; this is helpful for quicker previewing of results.
Hope this helps!