Gain dynamics and corresponding refractive index changes in fiber amplifiers are important for low noise fiber amplifiers and when using doped fibers as phase actuators. Furthermore self-induced refractive index changes are a possible explanation for mode fluctuations in high power fiber amplifiers, which currently present a major challenge for high power fiber lasers. Since these processes are all time dependent, a dynamic model of the refractive index change is very important. We will present measurements of phase shift dynamics in a low power ytterbium fiber amplifier. Using a simplified analytic model, which was originally developed to predict power modulation in telecom amplifiers, we were able to model the part attributed to the Kramers-Kronig-Relations and to obtain a much better understanding of the involved timescales. This will help modeling of phase noise in low noise amplifiers and possibly mode fluctuations in fiber amplifiers.