Here are my pictures to help describe this. So you have foamcore material (dark red are the paper coating and pink is the inner foam "core).
What I found happened when trying to cut all the way through in one pass, was you had to increase the laser power and go slower as the laser had to vaporize the top layer, foam, and bottom layer. This dumped a lot of heat near the foam and caused it to retract beyond the paper (essentially the paper has one kerf thickness and the foam has a different kerf thickness).
So, if the first vector cut would only cut through the top paper layer, the power and speed could be set such that heat build up would be less.
Then the second vector cut would only cut through the foam (this would probably be a faster speed and lower power vector cut).
Then lastly, the third cut would go through the back/bottom paper coating.
I’m not knowledgeable enough as to know if this really is what’s causing the kerf in the foam to not be so large when using three passes to cut through, but in my mind that is what’s going on. I can tell you though from experience that these are the observations I saw when using this material and procedure!