I believe I found a fix to this issue, which we just noticed with some new iPads introduced into the environment.
SharePoint 2010 parses the browser's user agent string to determine compatibility with various features - and it interprets Safari's " AppleWebKit/600.1.17" string as version 60, rather than version 600, due to a bad job of writing a regex. Version 60 is apparently an ancient version of Safari that cannot handle tab link bar thingy, so SharePoint sends a rendering as you describe. The fix is to create an entirely new .browser file (for example, called SafariFix.browser) and put it in the App_Browser folder off the site's IIS backend, and assuming the .browser file is configured correctly it'll override IIS's understanding of what version 60 of Safari is capable of, and will therefore send a full-feature version of the site to newer Safari browsers.
Please note that I have not fully tested this particular file at this time - I only just now found this after some inexact searching, while this unresolved support forum post was at the top of my searches, so wanted to update it with information that is hopefully helpful to others.
<?xml version="1.0" encoding="utf-8"?>
<browsers>
<browser id="Safari6FixOct2014" parentID="Safari60">
<identification>
<capability name="appleWebTechnologyVersion" match="6\d\d" />
</identification>
<capture>
</capture>
<capabilities>
<capability name="ecmascriptversion" value="1.4" />
<capability name="w3cdomversion" value="1.0" />
<capability name="supportsCallback" value="true" />
</capabilities>
<controlAdapters>
<adapter controlType="System.Web.UI.WebControls.Menu" adapterType="" />
</controlAdapters>
</browser>
</browsers>