To address empirical robust-parameter selection and insufficient feedback on tail economic risk in low-carbon dispatch of integrated energy systems under source-load uncertainty, a dispatch decision method combining two-stage robust optimization with posterior CVaR evaluation under laddered carbon trading is proposed. For a given uncertainty budget Γ, the method first establishes a robust dispatch model considering equipment operation, source-load uncertainty sets, and laddered carbon-trading costs to obtain the day-ahead schedule. Then, intraday adjustment costs are evaluated based on Latin hypercube sampling scenarios, conditional value-at-risk is used to quantify tail economic risk, and global RRPC together with adjacent-Γ marginal RRPC is employed to identify the trade-off among economy, low carbon performance, and robustness. Case studies show that the proposed method can reduce tail economic risk under adverse disturbances and provide a traceable quantitative basis for uncertainty-budget selection.