Assessing cultural alignment has become a key part of developing large language models (LLMs). Most existing evaluations treat culture as a single snapshot, checking only whether a model accurately depicts a society at the present moment. Cultural psychology, however, shows that values shift at varying rates and directions over time, so a truly "culturally aware" model should capture both the current state and its historical trajectory.\ \ This study leverages more than two decades of World Values Survey data to trace the cultural paths of 40 countries on the Inglehart‑Welzel map, and compares these trajectories with those generated by four state‑of‑the‑art LLMs. The findings reveal that while models generally place countries near their most recent surveyed positions, they tend to lag by several years, underestimate the magnitude of change, introduce movement where little occurred, and rarely reproduce observed reversals. This temporal flattening indicates that snapshot accuracy alone provides an incomplete picture of cultural awareness in LLMs, with implications for model evaluation, representational harms, and the governance of culturally sensitive AI systems.\ \ Review