Any trainer company that I have seen, recommends using alcohol to clean the rubber off. It's also a good idea to simply clean it off from time to time.

I always save my road tires that are worn out, and use them on the trainer. I know that there are specific trainer tires out there, but I see no reason to not use old tires. I do not have any heat build up, rubber on the trainer and it's a great way to get rid of them. Having been on a trainer now for over 25 years, I don't see any reason to spend money on tires unless they are new!