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I get notifications of new comments to certain articles on my site, so in short, no I do not have this problem.
Now if you are viewing an article and someone post a comment while you are viewing, it will not show on your screen until you make another server request (refresh or switch page).
The reason for this is when viewing a webpage you do not have a persistent connection to the server. Your browser requests the page, downloads the file of the page. So you are viewing the file as it was at the time of the request on your local computer (a file in your temporary internet files folder).
When you refresh your browser requests and downloads the updated file (with additional comments) from the server, then again disconnects from the server for your local viewing.