The Issue Comment Component (Aura/VisualForce) will only be able to display the default connection’s issues.
The "Auto-create" and "Auto-associate" only work for the default connection. "Auto-push" will push to all connections.
Related content
Is there any difference in setting up the integration in Jira for the multi-site feature?
How do I connect more than one Jira connection in my Salesforce environment?
How to view, create and associate Jira Issues from Salesforce by switching the Jira connection?
Are attachments sync configurations configured individually for multiple Jira site integration?