Hi, and welcome to Mixbvibes
I've taken a quick look at the specifications of your mixer, and it appears that you can only connect to your computer to (a) find music files to play through the mixer, or (b) record the output of the mixer to the computer. It doesn't seem like you can control Mixvibes using that particular model. I found this information:
The PS3-USB takes the top-selling functionality of Gemini’s original PS Series a step further by incorporating a USB I/O for connecting a Mac or PC, allowing you to play songs right from your computer’s music libraries. You can also use the PS3-USB to record directly into a DAW like Audacity, GarageBand, Cubase or Pro Tools (version 9 or later), ensuring your best performances are captured and stored right on your computer.
However, you would be able to use it to control the output from your computer to your speakers, as long as you have a multi-channel soundcard in your system.
To do this, select FILE - PREFERENCES - AUDIO from the menu, then select your soundcard from the top drop-down box. Then select EXTERNAL MIXER from the Routiing Mode Drop-down box.
You then need to assign your outputs, selecting different channels for the left and right decks. If you are unable to do this, then a small program called Asio4all is freely available which will allow you to use that instead. Simply install it, and select it in the top drop-down box. Next to the box there is a Control Panel button to configure Asio4all to use all all the channels you will need.
If my description is a bit confusing, or my information is wrong in any way, I apologise! Please don't hesitate to ask for further help - we are all here to help, and I'm sure you'll get it working quite easily.