If I am not mistaken, Numidium was powered by the soul of Zurin Arctus. Now, is that all it needs? A powerful soul? Or does it take more than that? I'm pretty sure Zurin was the battlemage so is his soul somehow infused with his powerful magicka?

^^He's also most likely a member of the Talos over-soul and Zurin Arctus was also going to ascend. Not to mention that Tiber was the one to stick his soul into the Mantella in the first place. Given that the first battery to power Numidium was the Heart of Lorkan... yeah, I don't think Numidium runs on ordinary souls.

There are a number of reason's why Tiber Septim's method for reactivating the Numidium worked. You're first going to want to take a good look at http://uesp.net/wiki/Lore:The_Arcturian_Heresy, which claims to expose Tiber's machinations and betrayals:

The Underking is the reanimated ghost of Ysmir Wulfharth, a Shezarrine, and (apparently) the author of this account, even though he uses the third person. It's sort of his power that activates the thing, being sort of Lorkhan. However, it's more complicated than that.

What Septim, Arctus and Wulfharth were effectively doing were re-enacting the betrayal of the enantiomorph, Lorkhan's murder by Auriel and Trinimac, as described in numerous http://www.imperial-library.info/content/monomyth. They're sort of tapping into the "mythical power" of this recurring drama. Wulfharth takes the place of Lorkhan, who was physically used in the original Dwemer model; the mantella becomes the Heart.

Also, Zurin's not just an ordinary battlemage. Like Wulfharth, he's a character that recurrs throughout history, according to Mannimarco in http://uesp.net/wiki/Lore:Where_Were_You_..._Dragon_Broke:

Mannimarco literally equates Zurin Arctus with Pelinal Whitestrake, a manifestation of Akatosh and (say it secretly) possibly a Shezarrine too. So there's all kinds of divine characters being manipulated and recapitulated in this event.