The proper way is to send the PDF, with the correct mime, and let the browser deal with it any way it decides to.

The stupid way for a site to act is to tell the browser to download the file instead of displaying it. And the stupid way for a browser to act is to do whatever the site tells it to do instead of what they user wants. The OP seems to have picked a stupid pair of tools.

Instead of opening it in the browser directly. They are dying from the extra clicks.