In this article, we extend the analysis of Diaz and Brevdo (J. Fluid Mech. 681:567-596, 2011) of the absolute/convective instability dichotomy at the onset of convection in a saturated porous layer with either horizontal or vertical salinity and inclined temperature gradients to studying the influence of the Soret effect on the dichotomy in a similar model. Only longitudinal modes are considered. We treat first normal modes and analyze the influence of the Soret effect on the critical values of the vertical thermal Rayleigh number, R (v), wavenumber, l, and frequency, omega, for a variety of values of the horizontal thermal Rayleigh number R (h), and the vertical salinity Rayleigh number, S (v). Our results for normal modes agree well with relevant results of Narayana et al. (J. Fluid Mech. 612:1-19, 2008) obtained for a similar model in a different context. In the computations, we use a high-precision pseudo-spectral Chebyshev-collocation method. Further, we apply the formalism of absolute and convective instabilities and compute the group velocity of the unstable wavepacket emerging in a marginally unstable state to determine the nature of the instability at the onset of convection. The influence of the Soret effect on the absolute/convective instability dichotomy present in the model is treated by considering the destabilization for seven values of the Soret number: S (r) = -1, -0.5, -0.1, 0, 0.1, 0.5, 1, for all the parameter cases in the treatment of normal modes.