have you reviewed the Customer Notification scheme and the project Notification scheme? Can you capture an image of your config? Also, are you saying there is no "Share with customer" and "Comment internally" buttons when an agent adds a comment?
In addition to making sure they are not on the Notification Scheme (no reporter) you should look at making sure they are not in the permission scheme either. The only way that you can block JIRA users from seeing internal comments is to remove them from the Browse Projects.
To make sure they cannot make internal comments, look at the Add Comments permissions in your scheme. Only roles/users/groups related to agents and "Service Desk Customer - Portal Access" should be there.
...be more productive while being fun to use at the same time. For some, getting started can be a bit intimidating. This is especially true if Jira Service Desk is your first exposure to Atlassian...
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