Yes, if you tick the download box the customer is taked to a download page at the end of payment process.
For the problem you faced, you can enable download in the product and then enter a your
site's URL or URL of a "thank you" page on your site in the "thank you URL" field in E-junkie Seller Admin > Preferences. That way, after the sale, buyer will be redirected to your website and to get the download, they'll have to use the download link we send them in the
email. So they can't use anyone else's email.