It's not made of foam. It's a delrin, (rubber) washer and
yes you put in on under the record. This forces the LP up
just a tad and allows the clamp to "press out" the
record at the edges on the platter for a flat fit.
From the manual:
Place the rubber washer over the spindle and gently push
it down so that it rests flat on the center of the platter.
Place the record to be played on the turntable. Take the
clamp and screw it down and tighten it enough that the
periphery of the record is brought in contact with the
platter. You will notice that over tightening will sometimes
result in the periphery lifting off again. Do not over
tighten.
After using the clamp system for a while, the proper
amount of tightening will become pretty much automatic.
The action of the clamp system is to provide uniform
compression of the record at the outer edge of the label
area. First, the periphery of the record is forced into
contact with the platter. Then, the rest of the grooved area
is pushed into contact.