Aside from being right- or left-handed, I think the method may depend on whether you are using the ruler lines to measure or whether you are using the cutting mat lines to measure.
Sounds like you are using the cutting mat lines to measure.
I was taught to use the ruler lines, so I use the ruler to measure from the fabric's cut edge (on the left) and then cut to the right of the ruler. The bulk of the fabric is to my right, but I am cutting the lefthand side of the fabric. (This would be exactly opposite for a left-hander.)