Evacuation conjecture for standard Young tableaux and vacillating tableaux

Let $Q$ be a standard Young tableau and let $V$ be its corresponding vacillating tableau. Let evacuation, also called the Schützenberger involution, act on $Q$, and let reversal act on $V$. Evacuation conjecture. Evacuation of $Q$ corresponds to reversal of $V$. The source provides no proof or resolution of this correspondence, so its general validity remains open.