Since the dawn of Dynamics CRM all users have been confused about which fields/columns are considered when a quick find is performed. For a regular user there is NO way to know what the search looks for, and it might even be fields not shown in the quick find view.
This can easily be solved if hovering the quick find bar would show a tooltip with the names of each of the search columns. E.g. “Quick find for contacts is performed for: First Name, Last Name & E-mail”.