I used a RMB (right mouse button) option signal and then set the rect_position to my global mouse position. That way the popup menu extended down from where the user clicked. (Context Menu)
$menu/Tree/Menu.rect_position = get_global_mouse_position()
$menu/Tree/Menu.visible = true
$menu/Tree/Menu.popup()
I don't see where you are setting the popup to visible in your code and you are using show() instead of popup(). Try this:
func GeneratePaths():
dock.get_node("Popup").visible = true
dock.get_node("Popup").popup()
print('clicked')