All carbon is going to produce dust (it's carbon dust, not ash). Sometimes it takes a lot of rinsing, but at some point any carbon, even the stuff that looks like charcoal, rinses clean in my experience.
What's the brand/make you're using? Quality definitely makes a difference in how much rinsing is needed, as rbursek is intimating.
If the dust coats things, then I might have some concern. If not, then no, I'd just try to rinse more. (Try a submersion method, like the way you clean uncooked rice before cooking.)