Transition metal dichalcogenides (TMDs) are known to support complex excitonic states. Revealing the differences in relaxation dynamics among different excitonic species and elucidating the transition dynamics between them may provide important guidelines for designing TMD-based excitonic devices. Combining photoluminescence (PL) and reflectance contrast measurements with ultrafast pump-probe spectroscopy under cryogenic temperatures, we herein study the relaxation dynamics of neutral and charged excitons in a back-gate-controlled monolayer device. Pump-probe results reveal quite different relaxation dynamics of excitonic states under different interfacial conditions: while neutral excitons experience much longer lifetime than trions in monolayer WS2, the opposite is true in the WS2/h-BN heterostructure. It is found that the insertion of h-BN layer between the TMD monolayer and the substrate has a great influence on the lifetimes of different excitonic states. The h-BN flakes can not only screen the effects of impurities and defects at the interface, but also help establish a non-radiative transition from neutral excitons to trions to be the dominant relaxation pathway, under cryogenic temperature. Our findings highlight the important role interface may play in governing the transient properties of carriers in 2D semiconductors, and may also have implications for designing light-emitting and photo-detecting devices based on TMDs.