Mildew on pillows is like mildew in a bathroom. If you want to get rid of it, spray with a diluted bleach solution (like 1 part bleach to three parts water) and let dry. The mildew should disappear before your eyes.
I think it is curious that you get mildew if there are in the spa and the spa is being sanitized as the sanitized water should not cause mildew to grow. Just like there is no mildew growing on the underside of the cover. But then I don't have pillows so maybe it is something unique about them.