The extent to which climate variability in Central Asia is causally linked to large-scale changes in the Asian monsoon on varying timescales remains a longstanding question. Here we present precisely dated high-resolution speleothem oxygen-carbon isotope and trace element records of Central Asia's hydroclimate variability from Tonnel'naya cave, Uzbekistan, and Kesang cave, western China. On orbital timescales, the supra-regional climate variance, inferred from our oxygen isotope records, exhibits a precessional rhythm, punctuated by millennial-scale abrupt climate events, suggesting a close coupling with the Asian monsoon. However, the local hydroclimatic variability at both cave sites, inferred from carbon isotope and trace element records, shows climate variations that are distinctly different from their supra-regional modes. Particularly, hydroclimatic changes in both Tonnel'naya and Kesang areas during the Holocene lag behind the supra-regional climate variability by several thousand years. These observations may reconcile the apparent out-of-phase hydroclimatic variability, inferred from the Holocene lake proxy records, between Westerly Central Asia and Monsoon Asia.