racksmith101 :
There should be a 4 pin connector that connects to your motherboards RGB header, the 3 pin connector connects to other RGB peripherals. It's next to step 4 in your case manual. http://www.phanteks.com/Eclipse-P350X.html
The '4 pin' connector from the case is only 3 pin in reality (one of the pin holes isn't wired).
The issue, as stated by the OP, is that the mobo supplies 12V on the RGB header while the associated RGB connector from the case expects 5V.
@morgankk other than returning stuff and getting components that are compatible out of the box, I don't know if there's any easy way to do this short of splicing cables and stuff.
If you want to connect the LEDs to you motherboard (which allows for software control of them), do you even need to connect them to your case though? You could just buy some 12V RGB LEDs that work with the mobo and connect them directly. You would lose the ability to control them manually via the buttons on the case though.