I don't think they really mean start, but rather layout. The N will be cut where the B was cut with the old cutter.
But yeah, you don't need to change your design, just the way you think of plotter orientation. You say it cuts right to left, but if you look at the cutter from the other side it's cutting left to right. If I'm reading correct, the bottom right corner will be the origin point on the cutter so that when the job is done you'd be able to read the words as the vinyl hangs from the cutter.
I don't know your software, but most programs you can change the orientation so that it will plot like your old one if you can't wrap your head around the different orientation.