AI-generated videos (AIGVs) have achieved unprecedented photorealism, posing severe threats to digital forensics. Existing AIGV detectors focus mainly on localized artifacts or short-term temporal inconsistencies, thus often fail to capture the underlying generative logic governing global temporal evolution, limiting AIGV detection performance. In this paper, we identify a distinctive fingerprint in AIGVs, termed anomalous temporal self-similarity (ATSS). Unlike real videos that exhibit stochastic natural dynamics, AIGVs follow deterministic anchor-driven trajectories (e.g., text or image prompts), inducing unnaturally repetitive correlations across visual and semantic domains. To exploit this, we propose the ATSS method, a multimodal detection framework that exploits this insight via a triple-similarity representation and a cross-attentive fusion mechanism. Specifically, ATSS reconstructs semantic trajectories by leveraging frame-wise descriptions to construct visual, textual, and cross-modal similarity matrices, which jointly quantify the inherent temporal anomalies. These matrices are encoded by dedicated Transformer encoders and integrated via a bidirectional cross-attentive fusion module to effectively model intra- and inter-modal dynamics. Extensive experiments on four large-scale benchmarks, including GenVideo, EvalCrafter, VideoPhy, and VidProM, demonstrate that ATSS significantly outperforms state-of-the-art methods in terms of AP, AUC, and ACC metrics, exhibiting superior generalization across diverse video generation models. Code and models of ATSS will be released at https://github.com/hwang-cs-ime/ATSS.