This happens only if users log in to the site with both browsers. The plugin keeps the information of unlogged users in a cookie, while it stores the information of logged-in users in the database. As cookies are stored in the browser, users have to log to the site to recover their recently viewed products.
Products will show on the detail page of any product, and everywhere you want using its widget and shortcode. Once installed, the plugin will install the “Recently Viewed Products” page, which you can use to easily show all recently viewed products of the user.