I always wash my white spirit soaked sponges in the machine with the bortex and oxygen bleach. My machine never acquires a white spirit smell...
If yours has like they suggest just do an empty boil wash in it, or better yet do an empty boil wash with some nice perfumed washing tablets.
I'd do it on a boil wash with a couple of shovels of oxygen bleach instead of some perfume detergent, but I don't know how white spirit would react with it. "Oxygen bleach" is very similar to hydrogen peroxide so I don't
think it will do any harm but you should ask a chemist lest I be responsible for your deaths