Actually it looks like those wires are correctly placed. The manual has all the information that you need to figure out how things should be. Sometimes the manual should not be trusted but in most cases it is correct. In this one it is correct.

Here's the relevant page of the manual.

01_manual.jpg

Here's the specific sections for the header/connector that you are looking for.

02_manual.jpg

Here is your wiring with annotation.

03_interconnect_board.jpg

Looks correct to me. Your connectors are not in good shape and need to be replaced but the wires are in the correct order.

I am a little confused as to what you're asking but I hope this explains it to you.

interconnect.jpg

Connections on a schematic are not necessarily in consecutive or contiguous order. You must always check the actual pin number. Sometimes the schematics are done this way to reduce the overlapping lines representing the connections that can be much harder to follow than numbers in a different order.