Below is a failing test for each. Reason seems to be simply a missing table.edit(newLocation) and tree.edit(treeItem) (as in ListCell)

The failing tests:

    public void testTableEditStartOnCellHasEditingCell() {
        TableView<TableColumn> control = createEditableTable();
        new StageLoader(control);
        int editIndex = 1;
        IndexedCell cell = getCell(control, editIndex, 0);
        // start edit on cell
        cell.startEdit();
        // test control state
        assertNotNull("editingCell on control must not be null", control.getEditingCell());
    }

    public void testTreeEditStartOnCellHasEditingItem() {
        TreeView<String> control = createEditableTree();
        new StageLoader(control);
        int editIndex = 1;
        IndexedCell cell = getCell(control, editIndex);
        // start edit on cell
        cell.startEdit();
        // test control state
        assertNotNull("editingCell on control must not be null", control.getEditingItem());
    }