How to apply focus for specific tab in quicktab
You can alter the search form hook_for_alter using form id.

Add a hidden field name it 'mytab' whose by default value will be channel and on click of tab its value will be toggled between channel and profile.

So when we submit the form to search the content, it will look this way ?title=hello&amp;mytab=channel

Now on in your hook_form_alter inline js code to select the default tab based on the mytab value that you can get using $_GET.

Let me know if it works for you.