Are the background images replaced?
Currently, ShortPixel Adaptive Images (SPAI) can replace the URLs of the images used as background only if they are included inline in the HTML of your website.
If the images are included in external CSS files, then SPAI won't be able to find and replace them.
In a future update the plugin will be able to replace those images as well.
A workaround for this is to use ShortPixel Image Optimizer (SPIO) and optimize with it only the background images. Deactivate then SPIO and only keep SPAI active and this way you'll have the background optimized.