No, that's exactly right. That's how Image Processor works. It always saves copies. This is functionality that I find REALLY useful when saving output jpegs (as you know from this video). But I agree it's a bit clumsy if saving initially-edited PSDs.
You want to know the absolute easiest way? Just hit Ctrl Alt W (or go to File>Close All). This will immediately bring up a message that says "File has not been saved, do you want to save it now?" Make sure you check the "Apply to all" box before hitting "Yes", and then it will go through and quickly save them.