Deep learning-based automatic modulation classification (AMC) is pivotal for intelligent spectrum sensing in the Internet of Things (IoT), yet its practical deployment faces synergistic threats from domain shifts and adversarial attacks. While existing methods typically address these challenges in isolation, they fail to resolve the intrinsic conflicts between feature alignment and robustness boundaries. To bridge this gap, we propose Progressive Uncertainty-Aware Active Robust Adaptation (PUARA), a progressive framework designed to integrate adversarial robustness into unsupervised domain adaptation (UDA) for AMC. PUARA employs a progressive strategy that uses uncertainty-screened target data to construct a geometric safety region, allowing the model to autonomously evolve defenses against target-specific vulnerabilities without ground truth labels. Extensive experiments on RML datasets demonstrate that PUARA significantly outperforms state-of-the-art baselines, achieving an average accuracy above 87.5%. Critically, the proposed active adaptation stage alone yields a performance boost of up to 12.63%, confirming the superiority of PUARA in ensuring secure and robust cross-domain IoT communications.