Would transactions/spring Transaction propagation solve this concurrency issue?

Few things need consider, DAO is focus on operation on single entity, and service is focus on operation of one or more entities, so the transaction should put on service layer, so you can reuse DAO's operation without any transaction, but let service to decide when start and end transaction.

Unless there's a method annotated with @Transactional further up the stack, they will be occurring in separate transactions, so yes you will have a potential for a race condition.

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