Is there a black rubber washer about 1-1/4" in diameter on the spindle? It goes on BEFORE the record and should stay in place. From the VPI website here is an FAQ regarding that washer:
"My VPI record clamp came with a rubber washer. What am I supposed to do with it? The rubber washer is meant to be permanently placed over the turntable's spindle below the record. This prevents "dishing" of the LP when it is clamped to the platter using the threaded VPI clamp."
Even with the washer there will be some distortion of the record as you tighten it, just don't tighten the clamp too much, you can dish the record. And by all means don't leave a record clamped for any length of time (like overnight) you can deform it permanently!