as per attached test case, note the context menu will fire the action listener only for the root node.
three test pages within this test app:-
                 <ace:linkButton id="linkButton1" value="12684" href="contextMenuInAceTree.jsf"></ace:linkButton>
                   <ace:linkButton id="linkButton3" value="12684Variation" href="contextMenuInAceTree2.jsf"></ace:linkButton>
                   <ace:linkButton id="linkButton2" value="12684 no ace ajax" href="contextMenuInAceTreeNoAceAjax.jsf"></ace:linkButton>
12684 is original test case.
12684 variation is not using static lists directly in page.
12684 no ajax is without using ace:ajax.

First two show js errors
"[window] Source element is undefined, cannot determine if this view is ICEfaces enabled." (once for each ace:ajax per menuItem). Note the id's that the ace:tree generates
javax.faces.execute: form:tree:-:0:1:-:menuItem3a
Even the showcase example shows '-' within id's of ace:tree. Is this acceptable for jsf id's?