If I get your query correctly, then you are willing to open the PDF file directly in Adobe Reader rather than saving it locally to your download folder.
Form where exactly you are getting those files, is it on web via Chrome or Firefox? Actually, this isn't Adobe Reader feature because Reader doesn't automatically decides whether files need to be opened or saved.
Its totally depends on the web browser you are using to view PDF. Like Chrome, it downloads the document first and then lets you open it. So you need to change your web browser.