The readme states that the appliance has to be upgraded to S12 before S13 can be loaded because S12 is a Service Pack containging a number of bug fixes while S13 is just signatures.
But this requirement for first upgrading to S12 is just for the appliance, and not for the director itself. The S12 on the director is just signatures which are already included in S13.
So you can upgrade the sensor appliance to S12 and then immediately upgraded to S13 (or the latest S15).
The Director however, can be directly upgraded to S13 (or the latest S15) without having to worry about S12 in between.
Marco