It's gonna take practice. Try not to stop the inner wheel, the more it turns, the less it chews. This of course means the outer wheel is turning even faster, making for a very quick turn. While learning the mower, that high speed turn isn't comfortable yet, but it will come with time.
I'm only on my 3rd or 4th season with my first zero turn, and I still make chew spots sometimes.
what you want to do is to back the lever from the inner wheel so it slow down, but still turn, I would also reccomend to slow down the outter wheel, but less then the inner wheel, so you can make a slow speed turn without tearing up the grass
Take is slower in turns. No need to make high speed, snap turns. Even the pros can't afford to put ruts in a client's lawn. Use an easy, smooth touch on those lap bars. You should be able to use minimal lap bar changes to negotiate even a 180 degree turn.