Currently, our connector receives the comments from Salesforce only, Comments from JIRA is not synchronized to Salesforce.
From my point of view, if JIRA is not visible to the Customer support, then there will an issue as the customer support will not be able to see the comments from JIRA.
It would be better if we can having something like salesforce (public/private) comments where private comments between JIRA should not be updated in Salesforce (if this is possible). Private comments are for the developers to make comments that are not meant to be seen by the customer support team. Where as the public comments are meant to be shared between two departments.
We do have feature request on this as the customer feels there's is a "must-have" feature.