Despite a few recent reports on Rashba effects in two-dimensional (2D) Ruddlesden-Popper (RP) hybrid perovskites, the precise role of organic spacer cations in influencing Rashba band splitting remains unclear. Here, using a combination of temperature-dependent two-photon photoluminescence (2PPL) and time-resolved photoluminescence spectroscopy, alongside density functional theory (DFT) calculations, we contribute to significant insights into the Rashba band splitting found for 2D RP hybrid perovskites. The results demonstrate that the polarity of the organic spacer cation is crucial in inducing structural distortions that lead to Rashba-type band splitting. Our investigations show that the intricate details of the Rashba band splitting occur for organic cations with low polarity but not for more polar ones. Furthermore, we have observed stronger exciton-phonon interactions due to the Rashba-type band splitting effect. These findings clarify the importance of selecting appropriate organic spacer cations to manipulate the electronic properties of 2D perovskites.