On https://github.com/Grandt/PHPZip/blob/master/src/Zip/Core/AbstractZipArchive.php#L743 and at various points in the documentation you refer to Content-Disposition: attached, and that is what is sent to the browser.
According to http://www.w3.org/Protocols/rfc2616/rfc2616-sec19.html and http://www.ietf.org/rfc/rfc1806.txt the allowed values are inline and attachment.