We report an analytical model and experimental validation of the temporal dynamics of 3-level system fiber amplifiers. The model predictions show a good agreement with the measured pump power to output power and the pump power to output phase transfer functions in an EDFA pumped at 976 nm, as well as with the typical literature values for the spontaneous lifetime of the involved energy levels. The measurements show a linear relation between the effective lifetime of the meta-stable level and the output power, and a filtering of the temperature-induced phase-shift due to the quantum defect at a sufficiently high frequency modulation.