Detect focus initiated by tab key?

I know you have accepted an answer but you could test the button pressed using the following:

$('#detect').on('focus', function(e){
    $(window).keyup(function (e) {
        var code = (e.keyCode ? e.keyCode : e.which);
        if (code == 9) {
           alert('I was tabbed!');
        }
    });
});

http://jsfiddle.net/LPGLm/1/

Edit: change the listener around:

$(window).keyup(function (e) {
    var code = (e.keyCode ? e.keyCode : e.which);
    if (code == 9 && $('#detect:focus').length) {
        alert('I was tabbed!');
    }
});

http://jsfiddle.net/LPGLm/7/

A more responsive solution would be to use two listeners:

var mousedown = false;
$('#detect').on('mousedown', function () {
    mousedown = true;
});

$('#detect').on('focusin', function () {
    if(!mousedown) {
        // logic
    }
    mousedown = false;
});

Fiddle showing the difference in speed:

http://jsfiddle.net/u2y45/1/

As you've noticed, the event object itself does not distinguish the means of access. What you can do is to bind a mousedown listener, which will fire before focus, and set some timestamp flag that you compare to some threshold value in your focus handler.