AmyMarie,
Sorry about taking so long to respond. But to answer your question NO, I have not had any problems with the black rubbing off. In fact I had just dyed some pieces for testing and when I saw your question I got a cloth soaking wet and started rubbing those pieces. I had a little bit, like very little bit mostly just excess pigment I think, but nothing like what you are describing. I am using pro-dye though, I do remember having a bit more trouble with the regular dye lifting off afterwards, one of the main reasons why I switched from the regular to the Pro-Dye. I also oiled before dyeing, hope this helps.