You are right that at zero bias there is only an equilibrium part of the contour integral. But at zero bias there is no current, so it's a rather uninteresting calculation. To compute any real device properties, you have to include the non-equilibrium part, at finite bias, to calculate the current. Please refer to M. Brandbyge et al., Phys. Rev. B 65, 165401 (2002) for the details.
So "the equilibrium transmission was evaluated with a Green's function method" is quite accurate, but of course at finite bias also the non-equilibrium part is computed using Green's functions. DFT is used to evaluate the Hamiltonian which goes into calculating the Green's function, but you could also use a semi-empirical Slater-Koster method, or DFTB.
