How much voltage does a 12V led strip need to light up?
What you are referring to depends on many things:  the length of your LED strip (how much wires in between LED's), the current consumption with each LED and the amount of current that your power supply can source. 

At first glance, any led strip/device requires the rated voltage no more no less. Issue often arise when the current requested by all the strip is way above what the wire can safely take without inducing voltage loss. 

You might think about increasing the voltage to counteract this effect of long LED strip with small wires, but it will not solve your issue completely. You run the risk of burning LED along the way or shorten their lifespan. Usually, the simplest approach would be to divide the LED into multiple shorter section and still provide it with 12v. This will reduce the wire voltage drop since the total current drawn per leg will be reduced. The only limitation become your power supply.

If you are using a per-packaged device (like the one you pointed out as an example), then the only thing you need to think about is your power source (yet again). Can it safely provide the required current for your device? If so, you're good to go.