Below is the following code from http://python-gtk-3-tutorial.readthedocs.org/en/latest/menus.html#example doesn't show tooltips on the MenuBar even though they are defined but show tooltips for other defined objects such as the ToolBar.

Another menu system designed in Glade showed the tooltips in the menu appropriately.

Here is the code that has been slightly modified from original:

#! /usr/bin/env python
# -*- coding: utf-8 -*-


from gi.repository import Gtk, Gdk

UI_INFO = """
<ui>
  <menubar name='MenuBar'>
    <menu action='FileMenu'>
      <menu action='FileNew'>
        <menuitem action='FileNewStandard' />
        <menuitem action='FileNewFoo' />
        <menuitem action='FileNewGoo' />
      </menu>
      <separator />
      <menuitem action='FileQuit' />
    </menu>
    <menu action='EditMenu'>
      <menuitem action='EditCopy' />
      <menuitem action='EditPaste' />
      <menuitem action='EditSomething' />
    </menu>
    <menu action='ChoicesMenu'>
      <menuitem action='ChoiceOne'/>
      <menuitem action='ChoiceTwo'/>
      <separator />
      <menuitem action='ChoiceThree'/>
    </menu>
  </menubar>
  <toolbar name='ToolBar'>
    <toolitem action='FileNewStandard' />
    <toolitem action='FileQuit' />
  </toolbar>
  <popup name='PopupMenu'>
    <menuitem action='EditCopy' />
    <menuitem action='EditPaste' />
    <menuitem action='EditSomething' />
  </popup>
</ui>
"""

class MenuExampleWindow(Gtk.Window):

    def __init__(self):
        Gtk.Window.__init__(self, title="Menu Example")

        self.set_default_size(200, 200)

        action_group = Gtk.ActionGroup("my_actions")

        self.add_file_menu_actions(action_group)
        self.add_edit_menu_actions(action_group)
        self.add_choices_menu_actions(action_group)

        uimanager = self.create_ui_manager()
        uimanager.insert_action_group(action_group)

        menubar = uimanager.get_widget("/MenuBar")
        print menubar

        box = Gtk.Box(orientation=Gtk.Orientation.VERTICAL)
        box.pack_start(menubar, False, False, 0)

        toolbar = uimanager.get_widget("/ToolBar")
        box.pack_start(toolbar, False, False, 0)

        eventbox = Gtk.EventBox()
        eventbox.connect("button-press-event", self.on_button_press_event)
        box.pack_start(eventbox, True, True, 0)

        label = Gtk.Label("Right-click to see the popup menu.")
        label.set_tooltip_text('This is the label tooltip')
        eventbox.add(label)

        self.popup = uimanager.get_widget("/PopupMenu")

        self.add(box)

    def add_file_menu_actions(self, action_group):
        action_filemenu = Gtk.Action("FileMenu", "_File", "This should be the tooltip", None)
        action_group.add_action_with_accel(action_filemenu, None)

        action_filenewmenu = Gtk.Action("FileNew", None, None, Gtk.STOCK_NEW)
        action_group.add_action(action_filenewmenu)

        action_new = Gtk.Action("FileNewStandard", "_New",
            "Create a new file", Gtk.STOCK_NEW)
        action_new.connect("activate", self.on_menu_file_new_generic)
        action_group.add_action_with_accel(action_new, None)

        action_group.add_actions([
            ("FileNewFoo", None, "New Foo", None, "Create new foo",
             self.on_menu_file_new_generic),
            ("FileNewGoo", None, "_New Goo", None, "Create new goo",
             self.on_menu_file_new_generic),
        ])

        action_filequit = Gtk.Action("FileQuit", None, None, Gtk.STOCK_QUIT)
        action_filequit.connect("activate", self.on_menu_file_quit)
        action_group.add_action(action_filequit)

    def add_edit_menu_actions(self, action_group):
        action_group.add_actions([
            ("EditMenu", None, "Edit"),
            ("EditCopy", Gtk.STOCK_COPY, None, None, None,
             self.on_menu_others),
            ("EditPaste", Gtk.STOCK_PASTE, None, None, None,
             self.on_menu_others),
            ("EditSomething", None, "Something", "<control><alt>S", None,
             self.on_menu_others)
        ])

    def add_choices_menu_actions(self, action_group):
        action_group.add_action(Gtk.Action("ChoicesMenu", "Choices", None, None))

        action_group.add_radio_actions([
            ("ChoiceOne", None, "One", None, None, 1),
            ("ChoiceTwo", None, "Two", None, None, 2)
        ], 1, self.on_menu_choices_changed)

        three = Gtk.ToggleAction("ChoiceThree", "Three", None, None)
        three.connect("toggled", self.on_menu_choices_toggled)
        action_group.add_action(three)

    def create_ui_manager(self):
        uimanager = Gtk.UIManager()

        # Throws exception if something went wrong
        uimanager.add_ui_from_string(UI_INFO)

        # Add the accelerator group to the toplevel window
        accelgroup = uimanager.get_accel_group()
        self.add_accel_group(accelgroup)
        return uimanager

    def on_menu_file_new_generic(self, widget):
        print "A File|New menu item was selected."

    def on_menu_file_quit(self, widget):
        Gtk.main_quit()

    def on_menu_others(self, widget):
        print "Menu item " + widget.get_name() + " was selected"

    def on_menu_choices_changed(self, widget, current):
        print current.get_name() + " was selected."

    def on_menu_choices_toggled(self, widget):
        if widget.get_active():
            print widget.get_name() + " activated"
        else:
            print widget.get_name() + " deactivated"

    def on_button_press_event(self, widget, event):
        # Check if right mouse button was preseed
        if event.type == Gdk.EventType.BUTTON_PRESS and event.button == 3:
            self.popup.popup(None, None, None, None, event.button, event.time)
            return True # event has been handled

window = MenuExampleWindow()        
window.connect("delete-event", Gtk.main_quit)
window.show_all()
Gtk.main()