I had this exact same problem when i first starting using a trainer. Try adjusting the resistance by pushing the tension knob on the back to push the trainer roller more onto your tire. The first few times i used my roller, i shred so much tire, i was finding it weeks later. I adjusted the trainer roller and it eliminated that problem.

This worked for me on my Cycleops Trainer and it might not work for you. But just thought i'd offer my experience.