Frequency modulation of narrow-linewidth lasers can cause coherent backscattering in cladding-pumped fiber amplifiers. This detrimental effect can be observed in Tm-based fiber amplifiers and can be an additional limitation for power scaling applications. We investigate such instabilities in Tm- and Tm/Ho-doped fiber amplifiers for a wide range of design parameters (active fiber length, pumping scheme, dopant type) and operation regimes (laser frequency tuning rate, amplifier gain). For each amplifier configuration, the backward-propagating (BP) signal is found to peak at a specific laser frequency tuning rate, with an amplitude and a frequency that increase with increasing amplifier gain and fiber length.