Interesting. As long as you wash it thoroughly the second time it looks like it would be fine. I have just always been taught not to use it for a cleaner, and some primers like the XIM mentioned in a previous post, specifically say in the specs Not to use mineral spirits for cleaning.
Also, the system in the link doesn't include the use of a primer.
An easy way to be sure would be to ask a SW rep where you bought the primer about cleaning instructions for that specific product.