Theoretically it's not possible but maybe this could work:
Basicly since it's the same website you can store a variable somewhere like in local storage in the tabB like this when ever you need to go back to tabA:
localStorage['update'] = true
Then on tabA where you opened the tabB following your example you can make an interval to check if it has to be updated or what ever with a setInterval function.
setInterval(function(){
if (localStorage['update'] == true){
localStorage['update'] = false;
$.get(location.href, function(){window.open(location.href)}, 'html');
window.opener = window;
window.close();
}
}, 5000);
So this will basicly check every 5seconds if it has to be updated, if yes then it sets the update back to false or it will keep refreshing the page, then it opens a new and close itself that will force the browser to focus on the new tab.
It's not exactly what you want to achieve but it's as close as you can get with js.
If you don't want to refresh instead of $.get(... you can just make an alert so the title of the tab will be bold so the user will know that something happens there.
I haven't tested this but you got the idea.