On small projects I birth, I have a little block of wood that I slip through the hole and first press the seam flat all the way around. I stick my arm through the hole to hold the bottom of the wood as I press. I then remove the piece of wood and press the edge flat. I will post a picture of my wood piece with the iron on top.
Pretend I have inserted it through the hole in the placemat and am holding it under the seam while I press carefully with my iron in my right hand.