The FeSe-based superconductors exhibit a wide range of critical temperature Tc under a variety of material and physical conditions, but extensive studies to date have yet to produce a consensus view on the underlying mechanism. Here we report on a systematic Raman scattering work on intercalated FeSe superconductors Lix(NH3)yFe2Se2 and (Li,Fe)OHFeSe compared to pristine FeSe. All three crystals show an anomalous power-law temperature dependence of phonon linewidths, deviating from the standard anharmonic behavior. This intriguing phenomenon is attributed to electron-phonon coupling effects enhanced by electron correlation, as evidenced by the evolution of the A1g Raman mode. Meanwhile, an analysis of the B1g mode, which probes the out-of-plane vibration of Fe, reveals a lack of influence by previously suggested structural parameters, and instead indicates a crucial role of the joint density of states in determining Tc. These findings identify carrier doping as the direct factor driving and modulating superconductivity in FeSe-based compounds.