Satellite edge computing (SEC) extends the capabilities of task offloading from the ground to near-Earth space by leveraging the wide coverage of satellites. However, the high-speed movement and long-range communication of satellites lead to Doppler shifts and signal loss, which can result in a high bit error rate (BER) and degrade communication link quality. As a result of the high BER, error correction is required, inevitably incurring additional delay during task offloading. Therefore, in this paper, we focus on the problem ofErrorCorrection awareDependencyTaskOffloading (EC-DTO) in satellite environments. By jointly considering task dependencies and BER-induced error correction delays, we formulate the EC-DTO problem as a constrained optimization problem with the objective of minimizing the makespan of users' tasks. To solve this problem, we propose APOS, which is an event-driven offloading framework based on task-AdaptivePrioritization andOptimistic-finish-time-based nodeSelection. Specifically, APOS adopts an online offloading framework that triggers scheduling upon task arrivals and completions with task dependency awareness. It iteratively updates task readiness and performs offloading decisions to reduce the overall makespan in the SEC environment. Simulation results show that APOS outperforms the representative methods, lowering the average makespan by 20.7% and the deadline violation ratio by 84.5% on average across all cases.