If you use the "default assignee" functionality, then that assignee will not get sent to Jira, even if that user exists in Jira. This could be considered a bug.
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If you set a feature or requirement in Aha! to be assigned to the default assignee, it will assign the corresponding issue in JIRA to the default assignee for the JIRA project.
If you want to have the feature or requirement assigned to a specific user, you need to use the specific user in Aha! - not the default user.