Tooltip: inputs with tooltips require two clicks to open on iOS

When using a JQuery UI tooltip on an input[type=text] and browsing from iPhone Safari, the user needs to click twice on the input in order to place the cursor inside the input text and be able to type.

The first click on the input only shows the tooltip (it does not open the keyboard and does not place the cursor inside the input).

Only the second click on the input, opens the virtual keyboard and places the cursor inside the input.

This can be reproduce on all the Tooltip demo pages http://jqueryui.com/tooltip/.

I tried:

tooltips.on( "tooltipopen", function(e, ui ) {
            var el = $(e.originalEvent.target || e.originalEvent.srcElement).closest($(this).tooltip('option', 'items'))[0];
            $(el).focus();
        });

But this helps only a little - with this code, clicking the input text works OK if the keyboard is closed (For example, when entering the first input with a tooltip or manually closing the keyboard (by clicking on the keyboard "Done" button) before clicking on the next input.

Environment:

iPhone 3Gs v6.1.2

Browser_UserAgent: Mozilla/5.0 (iPhone; CPU iPhone OS 6_1_2 like Mac OS X) AppleWebKit/536.26 (KHTML, like Gecko) Version/6.0 Mobile/10B146 Safari/8536.25