High-Q Si ring resonators play an important role in the development of widely tunable heterogeneously integrated lasers. However, while a high Q-factor (Q > 1 million) is important for ring resonators in a laser cavity, the parasitic high-power density in a Si resonator can deteriorate the laser performance at high power levels due to nonlinear loss. Here, we experimentally show that this detrimental effect can happen at moderate power levels (a few milliwatts) where typical heterogeneously integrated lasers work. We further compare different ring resonators, including extended Si ring resonators and Si3N4 ring resonators and provide practical approaches to minimize this effect. Our results provide explanations and guidelines for high-Q ring resonator designs in heterogeneously integrated tunable lasers, and they are also applicable for hybrid integrated butt-coupled lasers.