The Servo Module is nominally rated to 5-7V only because that's what most hobby servos are rated to. If you're using it to drive LEDs you don't need to worry about the voltage limit, but that's a good instinct. In this case it actually doesn't matter, though.
Backing up a few posts to address your earlier questions:
On this kind of LED strip, three wires control the R, G, and B channels. The other is either common power for the whole strip or common ground for the whole strip. This means that you'll need to wire it in one of two ways. Luckily, there's no penalty for hooking up this kind of LED strip backwards.
Test how to power the strip
Find a source of +12V DC power. If you don't want to cut the plug off your favorite adapter, verify that your plug is the right size and grab one of these barrel jack to screw terminal adaptors. Connect the +12V wire to one of the colored wires and the ground wire to the black wire. If it turns on, good, if not, switch the polarity and try again. If the channel you tried turned on for one configuration, all the others will behave the same way.
Controlling the LEDs using the Relay Module
If you want to use the Relay Module to control the LEDs, then @pcnate is right that you'd need two of the modules to allow you to turn all three channels on and off. In order to do so, you should connect the common lead, be it power or ground, to the power supply. Connect the other lead to one side of each relay and the colored wires from the LED strip to the other side. For a common anode (power) strip, this means you'd route ground to one side of each relay, connect one colored wire to the other side of each of the three relays, and connect the black wire directly to +12V. When you turn a relay on, the lights on that channel will illuminate.
Note that it's bad for the relays to switch on and off too quickly. Sadly, the relay datasheet fails to specify how fast is too fast, but I'd air on the side of caution and say that if you're switching more than once a second you're not using the right tool for the job.
Also note that with relays the strand is either on or off, not dimmable.
Controlling the LEDs using the Servo Module/Tessel's PWM
If you want instructions on how to use the Servo Module or Tessel's built-in PWM, I'm more than willing to write them up, but fair warning that the stock hardware will not be able to drive your 12V LEDs. You'll need to either hack the controller that came with the LEDs or find some power transistors. Either way, it'll require a little soldering. @jon is right, though: the code for it is super simple.