This study uses Shanghai Crude Oil Futures (SC) as a proxy for the upstream segment of China’s petrochemical industry and investigates how its market efficiency influences five key downstream product markets. Considering that markets differ in how they absorb information and in their structural features, we employ the Feasible Exact Local Whittle (FELW) estimator to construct a continuous market efficiency index. To capture efficiency dynamics across different time horizons, the study applies the Maximal Overlap Discrete Wavelet Transform (MODWT) to decompose the efficiency series into short-, medium-, and long-term components. These are then examined by Quantile-on-Quantile (QQ) regression to trace the varying marginal effects across different efficiency states. The results reveal strong state dependence and structural differences in the efficiency transmission from SC to downstream markets. Among the five markets, Low-Sulfur Fuel Oil and Asphalt exhibit the most stable transmission patterns, with the former showing a “saddle-shaped” structure and the latter following a “dual-path” pattern. In contrast, the links between SC and the markets for Linear Low-Density Polyethylene and Polypropylene are highly nonlinear and less predictable. Purified Terephthalic Acid demonstrates a dual mechanism of efficiency resonance and long-term anchoring. These findings deepen our understanding of information efficiency within industrial value chains. They also offer practical insights for managing market risk, guiding price policies, and designing regulatory frameworks in the energy sector.