<p>This study investigates the tumor–immune dynamics during dendritic cell therapy, incorporating the delays associated with negative feedback in tumor progression and the activation lag of effector cells in targeting tumor cells. The analysis confirms the positivity and boundedness of the solutions. Under specific conditions, the tumor-free equilibrium demonstrates global asymptotic stability. The distribution of equilibria and bifurcation diagram show that the system exists a backward bifurcations. The existence conditions for both local and global Hopf bifurcations at the positive equilibrium are established under identical delay conditions. The study highlights that the negative feedback delay significantly influences the ultimate stability or instability of the equilibrium and the potential occurrence of stability switches, an aspect previously under explored in the literature. Using the crossing curve method, the stability transition of the positive equilibrium is plotted in the two-delay plane. Periodic oscillations in populations emerge as the delays surpass certain critical thresholds, leading to the loss of stability at the positive equilibrium. These theoretical insights are corroborated by clinical data-driven numerical simulations. According to numerical examples, the equilibrium of system can go through the following phases when two delays select distinct values: stable to unstable, unstable to stable and back to unstable, or unstable to stable to unstable and finally unstable. Although the phenomenon of stable switches may manifest, the equilibrium may eventually prove to be unstable or stable.</p>