Likely an edge on the rest is snagging the fletch on release. A slight bevel on the belly side of the rest mat might reduce it. Is it glued down all the way to the edge? I suppose, without actually having seen it before, that it might have to do with the nock height, but I kinda doubt it. Is the nock positioned correctly for the #### feather?
Some Duco cement might fix your ripped fletching, at least for target shooting needs.