Emails are automatically being merged into existing tickets instead of creating new tickets, even though the user says they composed a new email.

Check the thread entry headers: open the merged ticket, click the dropdown arrow on the merged entry's blue bar and select 'View Email Headers'. Look for In-Reply-To or References headers -- if either is present, the email was a reply rather than a new message, regardless of what the user claims. If those headers exist, osTicket correctly threaded it as a reply.