Spatial crowdsourcing (SC) services, such as ridesharing and food delivery, are increasingly shaping people's daily lives. A key issue in SC is online task assignment, which involves assigning tasks to appropriate workers in real time. Most existing studies focus on task assignment within independent platforms but still face the limitation of spatial-temporal imbalance between tasks and workers. Recently, aggregation platforms (e.g., AMap's ride-hailing) have emerged, enabling tasks to be completed by workers from multiple cooperating platforms. However, effectively incentivizing these cooperating platforms to deliver high-quality services remains an open challenge. In this paper, we study a novel Aggregative Online Task Assignment (AOTA) problem, where the aggregation platform assigns tasks to suitable cooperating providers with the goal of maximizing overall quality-aware social welfare. To address the AOTA problem, we design an efficient Context-aware Online Bidding Task Assignment (COBTA) framework, which integrates a reverse sealed Vickrey auction to promote truthful bidding for public tasks among platforms. COBTA employs an exploration-exploitation strategy for efficient and effective public task assignment and leverages a multi-agent reinforcement learning method to enable cooperating platforms to make adaptive bid-or-not decisions based on their internal status. Extensive experiments on three real-world datasets validate the effectiveness and efficiency of our proposed solution.