I agree, fat can't turn into muscle -- it's physically impossible.
However, if it WAS possible, it would be a wonderful thing!! Unfortunately, we have to work for our muscle.
I started both cardio and weights at the same time, and totally believe that's the winning combination for fat loss. Cardio to burn calories, weights to build muscle to sustain our metabolisms and let us look great when the fat is gone. You are 100% doing it right by doing both from the beginning.