Eco-feedback interventions have been shown to influence user behavior in thermostat adjustments, promoting energy conservation in residential communities. Understanding user-thermostat interactions is critical for designing effective energy-saving strategies. This study develops and applies behavior-based metrics to quantify how residents interact with thermostats in response to an eco-feedback intervention. The intervention included personalized energy-saving tips, a social competition, and financial incentives to promote more efficient setpoint usage. Using high-resolution behavioral data collected from smart thermostats in a multi-unit residential community, the proposed metrics measure both the frequency and persistence of thermostat adjustments. These metrics provide detailed insights into user engagement, revealing significant variation in behavioral responses. Specifically, users exhibited varied patterns: some did not change how they interacted with the thermostat even with incentives, while others began adjusting schedule setpoints, temporarily using hold mode, or increasing the frequency of system-off actions—especially after incentives were introduced or increased. The findings suggest that behavior-specific evaluation approaches can help capture behavioral changes. This work highlights the potential of targeted behavioral metrics in assessing the impact of eco-feedback strategies.