Swarmling
Where/How does the green cable plug in?

There is both a 1/4 inch to 3.5mm adapter or a RCA to 3.5mm adapter included with the Nu Audio card. You can use either to plug into either the headphone jack or RCA jacks.

DMinnitti
You need to use the RCA splitter.
 
While the 1/4 inch/headphone port sounds better, the tiamat does its own bass crossover and sound routing on the hub, if you use the headphone port bass from the front left and right won't be delivered to the subwoofer. 

To be clear, it won't really matter much because the NuAudio card does not offer a crossover frequency to move the low-frequency content for the subwoofer to the C/Sub output. This is why many of us (including me) are complaining to EVGA in the hope they'll give us a proper crossover so that our subwoofers will actually mean something. File that under sad but true. I'm hard pressed to believe they shipped the 7.1 pro version without a crossover. It's crazy.