Sidechain techniques improve blockchain scalability and interoperability, providing decentralized exchange and cross-chain collaboration solutions for Internet of Things (IoT) data across various domains. However, current state-of-the-art (SOTA) schemes for IoT multi-domain data exchange are constrained by the need for synchronous networks, hindering efficient cross-chain interactions in discontinuous networks and leading to suboptimal data exchange. In this paper, we propose AsyncSC, a novel asynchronous sidechain construction. It employs a committee to provide Cross-Blockchain as a Service (C-BaaS) for data exchange in multi-domain IoT. To fulfill the need for asynchronous and efficient data exchange, we combine the ideas of aggregate signatures and verifiable delay functions to devise a novel cryptographic primitive called delayed aggregate signature (DAS), which constructs asynchronous cross-chain proofs (ACPs) that ensure the security of cross-chain interactions. To ensure the consistency of asynchronous transactions, we propose a multilevel buffered transaction pool that guarantees the transaction sequencing. We analyze and prove the security of AsyncSC, simulate an asynchronous communication environment, and conduct a comprehensive evaluation. The results show that AsyncSC outperforms SOTA schemes, improving throughput by an average of 1.21 to 3.96 times, reducing transaction latency by 59.76% to 83.61%, and maintaining comparable resource overhead.