We study the formation of the Stokes profiles of the He I multiplet at 10 830 Å when relaxing two of the approximations that are typically considered in the modeling of this multiplet. Specifically, these are the lack of self-consistent radiation transfer and the assumption of equal illumination of the individual multiplet components. This He I multiplet is among the most important for the diagnostics of the outer solar atmosphere from spectropolarimetric observations, especially in prominences, filaments, and spicules. However, the aptness of these approximations is yet to be assessed, especially in situations where the optical thickness is on the order of one (or greater) and the radiation transfer has a significant impact in the local anisotropy as well as the ensuing spectral line polarization. This issue becomes particularly relevant in the ongoing development of new inversion tools that take into account multi-dimensional radiation transfer effects. To relax these approximations, we generalized the multi-term equations for the atomic statistical equilibrium to allow for a differential illumination of the multiplet components and implement them in a one-dimensional (1D) radiative transfer code. We find that even for this simple geometry and relatively small optical thickness, both radiation transfer and differential illumination effects have a significant impact on the emergent polarization profiles. These effects should be taken into account in order to avoid potentially significant errors when inferring the magnetic field vector.