A popup-menu of a tree-buffer can be activated from keyboard with the
command tree-buffer-show-menu-keyboard which is bound to
M-m in every tree-buffer. How the popup-menu is displayed
depends if this command is called with a prefix-argument or not:
If called without a prefix-arg then the popup-menu is displayed graphically as if it would be activated via mouse (for GNU Emacs this works perfectly but for XEmacs there is a bug which results in a wrong menu-position - but the menu itself works also with XEmacs).
If called with a prefix-arg (C-u M-m) then the popup-menu is displayed with the tmm-mechanism (like the Emacs-[menu-bar] is displayed when `tmm-menubar' is called). This tmm-display is only available for GNU Emacs.