The transition voltage of three different asymmetric Au∕poly(phenylene) thiol∕Au molecular junctions in which the central molecule is either benzene thiol, biphenyl thiol, or terphenyl thiol is investigated by first-principles quantum transport simulations. For all the junctions, the calculated transition voltage at positive polarity is in quantitative agreement with the experimental values and shows weak dependence on alterations of the Au-phenyl contact. When compared to the strong coupling at the Au-S contact, which dominates the alignment of various molecular orbitals with respect to the electrode Fermi level, the coupling at the Au-phenyl contact produces only a weak perturbation. Therefore, variations of the Au-phenyl contact can only have a minor influence on the transition voltage. These findings not only provide an explanation to the uniformity in the transition voltages found for π-conjugated molecules measured with different experimental methods, but also demonstrate the advantage of transition voltage spectroscopy as a tool for determining the positions of molecular levels in molecular devices.