In this work, we focus on quantum correlations, specifically entanglement, quantum steering, and Bell nonlocality within the Tavis–Cummings model. This study investigates these quantum correlations in the context of various fields existing in the cavity. The findings reveal the hierarchy of quantum correlations—entanglement, quantum steering, and Bell nonlocality—in two two-level atoms under the influence of thermal, coherent, and squeezed vacuum states. The dynamic process demonstrates certain oscillations, with particular emphasis on the presence of asymmetric quantum steering.