Good morning, I'm not really sure how Reply/Private Note works. But I'm assuming private notes can only be seen be myself or other Techs. And regular Replies can be seen by anyone to include the original requester.
This is what the requester sees after submitting a ticket and after Techs have been entering notes
HelpDesk uses standard SharePoint permissions (Site Settings -> Site Permissions page). Any user that has access to Help Desk site can see everything that allow their permissions.
If a user has access to HelpDesk site and is allowed to see public comments they also will be able to see private comments.
By design, HelpDesk is for agents and requesters are supposed to submit tickets by email or via HelpDesk widget.
HelpDesk web widget is an entry point for non-agent users and help desk is a workspace for agents. The widget allows requesters to review their tickets, add comments and attachments.
HelpDesk. You may find more information about the widget here.