I rewrote the tab function as html (you can see the code on the site). All that is required is a little javascript to achieve the desired behaviour. I am using the browser's local storage object to return to the active tab. This works just like hitting the back button on the browser. Another way to do this is with a data toggle in Bootstrap, which is baked into to Joomla.
$(document).ready(function(){
$('a[data-toggle="tab"]').on('show.bs.tab', function(e) {
localStorage.setItem('activeTab', $(e.target).attr('href'));
});
var activeTab = localStorage.getItem('activeTab');
if(activeTab){
$('#myTab a[href="' + activeTab + '"]').tab('show');
}
});
This doesn't work with your Tabs addon. This only works by writing the HTML for the Tabs.
This is basic, basic functionality and I am stunned that this is not part of your "Tabs" addon. Hope this helps someone else and that you guys will add this or something like it in the future,