??
I don't understand how these things connect together.
How does the 12V power connect to the 5V controller?
I'm pretty sure these parts are not compatible.
*Do not plug those lights back into the board as you are drawing power amperage than rated through parts of the board and could DAMAGE IT.
Personally I would look at an entire kit like the "RGB Strip" that has parts that all work together.
Other:
I think maybe your confusion is that I think the "RGB Strip" page shows a WHITE power device that appears to be a 12Volt to 5V converter. So the 12V source (AC or the MOLEX adapter) plugs into that, and then you get 5V (via a USB connection) up to some maximum Amperage which I can't read.
So I think you're missing that unit which you would plug the strip into and NOT into the motherboard.
(I may have some things wrong as it's hard to see the connections in the pictures)
Also not sure how the REMOTE works but it looks like one end of the "Controller" is a receiver for the remote. So one end is power, one end is a receiver, and the other is where the strip plugs into... the receiver should just send signals to control how much power each LED strip gets.