You want to open PDFs from within your web browser in PDF Annotator, but another program opens within the browser.
This depends on your browser configuration, and on third party tools installed. For example, Adobe® Reader® installs a browser plugin, and registers itself to display PDF documents within the browser. To disable that, start Adobe® Reader®, go to "Edit, Preferences, Internet" and disable the "Display PDF in browser" option. You will have to restart your browser after that. In PDF Annotator, go to Extras, Settings, Integration, Exlorer and press the "Set as default viewer for PDF documents" button, then OK. The button will be inactive if you have already set PDF Annotator for default. Now, when you navigate to a PDF in your browser, you will get the download prompt like for any downloadable file, instead of the file being displayed in the browser. You can then select "Open" to open the document with PDF Annotator.