Measurements of fusion cross-sections of ⁷Li and ¹²C with ¹⁹⁸Pt at deep sub-barrier energies are reported to unravel the role of the entrance channel in the occurrence of fusion hindrance. The onset of fusion hindrance has been clearly observed in ¹²C +¹⁹⁸Pt system but not in ⁷Li+¹⁹⁸Pt system, within the measured energy range. Emergence of the hindrance, moving from lighter (^6,7Li) to heavier (¹²C,¹⁶O) projectiles is explained employing a model that considers a gradual transition from a sudden to adiabatic regime at low energies. The model calculation reveals a weak effect of the damping of coupling to collective motion for the present systems as compared to that obtained for systems with heavier projectiles.