I've never heard of such an issue with Mac/Safari, so i've no clue about this and i'm not able to suggest you a possible fix or why this is happening at your end. Safari normally just behaves like any other browser.

BTW if you are able to open the Safari error console and find out some js error, just let me know and maybe i could understand something more. If there are no errors, my only thoughts could be related to some addon or special feature of Safari blocking/suspending the network traffic thus preventing the chat to auto-update.

The version of Joomla or PHP obviously doesn't matter at all.