I don't think the sinks inside the Corian counter tops are Corian. I believe they are some kind of plastic. They will stain but add some bleach into a sink full of water gets ours looking like brand new effortlessly.
I add some bleach into water-filled sinks and toilet, let sit a bit to clean them, then drain all into the holding tanks as part of my fall disinfecting/deodorizing for winter storage in our under-the-house garage. Disinfecting the entire waste system prevents sewer gas from forming, then getting into the house.