Serializability (SER) and snapshot isolation (SI) are widely used transactional isolation levels in database systems. The isolation checking problem asks whether a given execution history of a database system satisfies a specified isolation level. However, existing SER and SI checkers, whether traditional black-box checkers or recent timestamp-based white-box ones, operate offline and require the entire history to be available to construct a dependency graph, making them unsuitable for continuous and ever-growing histories. This paper addresses online isolation checking by extending the timestamp-based isolation checking approach to online settings. Specifically, we design Chronos, an efficient timestamp-based offline SI checker. Chronos is incremental and avoids constructing a start-ordered serialization graph for the entire history, making it well-suited for online scenarios. We further extend Chronos into an online SI checker, Aion, addressing several key challenges unique to online settings. Additionally, we develop Aion-SER for online SER checking. Experiments highlight that Chronos processes offline histories with up to one million transactions in seconds, greatly outperforming existing SI checkers. Furthermore, Aion and Aion-ser sustain a throughput of approximately 12K transactions per second, demonstrating their practicality for online isolation checking.