Theurgy has strong religious overtones… but the moment described as sacrifice and hedged round with ritual is the Harrowing, not the moment when the blood gets used.
The Theurges sit above the priestly hierarchy (see the reverence with which Zebed treats Chirex) and their abilities are seen as an Angelic gift, so to society in general the Angels’ power (emanating from Unmoved Xthonos) is clearly what fuels Theurgy.
However, there isn’t a widely articulated sense that each time a Theurge pours blood into her palm, she’s propitiating the Angels.
As for how it all really works? Midichlorians.