Item parameter drift (IPD) poses a persistent threat to measurement validity in computerized adaptive testing (CAT). While cumulative sum (CUSUM)-based online calibration methods have shown promise for real-time IPD monitoring within the item response theory (IRT) framework, their application to cognitive diagnostic CAT (CD-CAT) remains limited. Moreover, conventional psychometric implementations of CUSUM control charts often rely on a fixed reference value that determines the minimum detectable drift size. This fixed specification limits adaptability to dynamic testing conditions, and the optimal magnitude of the reference value is generally unknown in practice. To address these limitations, this study introduces adaptive CUSUM charts that dynamically update the drift magnitude using exponentially weighted least squares and exponentially weighted moving average. Both univariate and multivariate variants are developed within a unified CD-CAT online calibration and monitoring framework. Two simulation studies and an empirical application to the LASSO Mechanics Cognitive Diagnostic dataset evaluate the proposed framework. Results indicated that all CUSUM charts outperformed the LRT in controlling false alarms. Among CUSUM variants, adaptive CUSUMs provided more conservative signaling for smaller IPD size and noisier residuals, while maintaining strong performance under abrupt drift, the dominant pattern in CD-CAT. Multivariate monitoring further improves robustness in operational settings. Effects of design factors, practical recommendations, methodological implications, and study limitations are discussed.