I bought a cheap trainer used and have searched online, but havent been able to find out how tight the tire should be on the tumbler. Ive been using it for a few weeks and its developed a nice layer of rubber where that tire touches it. Does that mean I have it setup incorrectly?

Someone else might be able to tell you if the layer of rubber is good or not -- I've been using a Vittoria trainer-specific tire on my Kurt Kinetic and in ~6mo/1000mi I've had very little residue left on the trainer. The tire itself quickly got a dark streak around its circumference, but it hasn't left that on the roller.

I set mine tight enough that the tire wouldn't slip (by listening for the squeak of the tire slipping) when putting in my hardest effort while sitting. When I start a sprint it'll squeak a bit during the acceleration, but settle down quickly.

Get a trainer tire. The skid marks are normal but you get more when you use non trainer tires.