It's very likely you connected one of the Purple START circuits to the NSS and the other to the starter relay/solenoid. I'm sure it's possible that either your NSS does not work, or that you got the wires wrong, but it seems just as likely you have the earlier Centech harness with two separate circuits.
Did you do the connections yourself? If so, do you remember the Purple wire being extra long and being able to reach the S post on the relay even after you cut it in half to splice into the switch? Or was it short enough that you had to add wire of your own?
If short, then it's probably the START wire intended for manual transmissions. If long, then that should be the correct one and so you'd want to look at the NSS again to see if it's functioning properly.
Do you have a test lamp or multi-meter to verify that the wires you used are only passing current in Park and Neutral? Either on the OHM setting or the DC Volt setting can work depending on how you test.
Not sure what the Blue wire would be, unless it's marked IGNITION or something like that. Centech has two or three different Blue wires that do different things for the ignition system. One might be for an ignition module power, one for ignition coil power, and one for a START signal most likely. And anything connected to the S post is expecting a START signal from the key.
But that's supposed to be the function of the "I" post instead. In my world I hate seeing anything but the Purple wire on the S post, but I know a lot of people do that and get away with it. Usually a fuel-injection system is looking for a START signal too, so that might be connected to the FAST setup.
the good news is that as you suggested, all the wires should be labeled along their length. Hopefully the installer used those appropriately!
Good luck.
Paul