First of all, if you're submitting low-resolution images, submit only JPEGs, (quality setting 8 or so) not TIFFs. TIFF is generally uncompressed, and file sizes are huge for electronic submission. There is no point in uncompressed image files when you have reduced them to 500 pixels.
Second, for pixel-based image files, always set image sizes in pixels, not inches. When downsizing, the pixel count is the primary limit on image quality, so get in the habit of changing pixel dimensions directly, not linear dimensions like inches or DPI. If you change the linear dimensions or the pixels per inch setting without checking the resample box in the size dialog, all you are doing is changing a tag in the file, and the pixel dimensions will not be changed. THat might be what is happening if your file sizes are >1MB for a 500-pixel JPEG. 100-200K should be the largest file for a JPEG that size.