I'm not familiar with these units, but it's designed for vehicle flasher systems. The box is likely not going to work unless there is a slow pulse of considerable current, such as what is produced by the vehicle flasher circuit. An SSR of the appropriate size, controlled by the LED-Wiz, could allow you to use the box if the output is pulsed like a car flasher. If you just want to use the individual LED units (they appear to have resistors in them already), I would approach it like this:
30w @ 12vDC = 2.5A, 2.5A/4 (the number of LEDs units) = 625ma per LED unit. This is pushing the envelope for the amount of current which can be directly pulled from a single pin on the LED-Wiz driver chip. However, if the software can synch multiple outputs to a single event, two of the outputs can be used together to get more current. It may work using only one output per LED unit for very short flashes, but it's really not recommended and would be putting the driver chip at risk. I certainly wouldn't try the single output approach without a heatsink on the driver chip, and some extensive testing to make sure it's safe.
Also be aware that the software you may be using to control the lighting, like any software, is not infallible and there could be instances where your PC locks up at the just the wrong time, leaving the light on for far longer than you expect it to. It's always a good idea to take this into account when deciding how to power these kinds of things.