I have a T3 synthetic is my barrel supposed to be free-floating because it is touching the stock?

Free Floating Barrel

There is no problem with your synthetic stocked rifle only wood stocked T3 models are completely free-floated.  Due to the stability of synthetic stocks the Tikka engineers have found that this rifle is more accurate with a light upward pressure applied to the barrel.  This is accomplished by molding a bump in the stock about 1/2 way up the barrel channel.  This could only be achieved with the synthetic stock since the wood stock will change dimensions slightly based on atmospheric conditions.