I think the prevailing theory back when I was in geology school (early '90s) was that kimberlite pipes were not associated with plumes, or at least we weren't sure enough to say. But it seems that may not be correct anymore. I read the petrology journal article you linked and it does indeed seem to attribute some connection to "ascending mantle flow". Not sure if that means the gigantic plumes which originate from the mantle core boundary, but it may. There is (may be) non-plume mantle movement as well; mantle gyres, I think they're called. If the ascending 'legs' of these gyres are under a craton, they would tend to create the extensional regime (continent trying to pull apart) that is necessary for kimberlite intrusion. Or maybe I'm completely wrong and should go back to using Wikipedia as a sole source of information rather than relying on my faulty memory.

But I don't think we have a real good picture of mantle dynamics yet.