It is not really connected like that.
I don't think closing the dialog should close the tab. You can start a search, then close the dialog
and the search continues and result is poping in into the list.
The only time I see a reason is if you return 0 result, but that would give the close of the dialog two very different behaviors.
sometimes it just closes the dialog, sometimes it closes the entire search module.
However if you close the tab.. the dialog will also be closed.