Given the complexity of multi-tenant cloud environments and the need for real-time threat mitigation, Security Operations Centers (SOCs) must integrate AI-driven adaptive defenses against Advanced Persistent Threats (APTs). However, SOC analysts struggle with countering adaptive adversarial tactics, necessitating intelligent decision-support frameworks. To enhance human-AI collaboration in SOCs, we propose a Cognitive Hierarchy Theory-driven Deep Q-Network (CHT-DQN) framework that models SOC analysts' decision-making against AI-driven APT bots. The SOC analyst (defender) operates at cognitive level-1, anticipating attacker strategies, while the APT bot (attacker) follows a level-0 exploitative policy. By incorporating CHT into DQN, our framework enhances SOC defense strategies via Attack Graph (AG)-based reinforcement learning. Simulation experiments across varying AG complexities show that CHT-DQN achieves higher data protection and lower action discrepancies compared to standard DQN. A theoretical lower bound analysis further validates its superior Q-value performance. A human-in-the-loop (HITL) evaluation on Amazon Mechanical Turk (MTurk) reveals that SOC analysts using CHT-DQN-driven transition probabilities align better with adaptive attackers, improving data protection. Additionally, human decision patterns exhibit risk aversion after failure and risk-seeking behavior after success, aligning with Prospect Theory. These findings underscore the potential of integrating cognitive modeling into deep reinforcement learning to enhance SOC operations and develop real-time adaptive cloud security mechanisms.