I use the june taylor rulers too as well as a number of other rulers. I too only use the mat for lining up. One thing I didn't see mentioned was that when I line up the ruler along the cut edge I include the width of the line. Makes a big difference.
Meaning when you line up that broken line on whatever measurement you want, include the space you can see between the breaks and align with the right edge of the black dash line.
I'm not all that perfect at anything, but I have a friend that is as perfect as you can get with everything she does (will tear out if it's 1 thread off) and that's the way she showed me to cut out.