This study examines how global turbulence factors shape volatility spillovers among emerging stock markets through the lens of risk cycles. We find that emerging market connectedness exhibits clear regime heterogeneity across risk cycles, while also preserving several persistent structural patterns. Specifically, trade policy uncertainty (TPU) and economic policy uncertainty (EPU) serve the dominant drivers during risk outbreak and risk accumulation periods, respectively. Meanwhile, sustainability uncertainty (ESGUI) consistently plays a leading driver role in both regimes, while physical climate risk plays a comparatively limited role. Furthermore, the effects of these core turbulence factors are nonlinear and threshold-dependent, highlighting the importance of accounting for risk cycle heterogeneity and nonlinear dynamics when assessing emerging market risk transmission.