Accurate characterization of tie-line power transfer capability is essential for ensuring the feasibility and optimality of cross-regional power exchanges. However, existing methods typically consider only the base operating scenario and neglect N-1 contingencies, leading to inaccurate assessments of regional tie-line transfer capabilities. This paper addresses this gap by focusing on the tie-line exchange capability of power systems under N-1 contingency constraints. A fast determination strategy is proposed based on the coupling relationship between the base case and N-1 scenarios, using a decomposition approach. Furthermore, the impacts of various generator control modes on tie-line exchange capability under N-1 contingencies are analyzed to support the optimal allocation of cross-regional power transfers. The proposed methods is validated using a provincial-level power system, demonstrating its accuracy and practical effectiveness.