Understanding the gain dynamics of amplification in rare-earth-doped silica glass fibers is crucial for developing sophisticated low-noise amplifiers and frequency combs. Recent and ongoing research efforts in these areas have specifically targeted the spectral region around 2 µm and the use of thulium-doped silica glass fibers as a broadband, power-scalable gain medium. We present a comprehensive characterization of the transfer functions of thulium ions in silica glass for emission in the spectral 2 µm region, including the magnitude and phase information. We investigated the most widespread pumping schemes: in-band pumping at 1550 nm, as well as out-of-band pumping at 790 nm. A semi-analytical model and a numerical model are developed to describe the complex energy level system of thulium ions and their associated ion-ion interactions, providing deeper insight into the influence of various parameters on the transfer functions of thulium ions in silica glass. The presented results of the transfer functions support the choice of fiber amplifier geometries and electronics to optimize noise performance.