So I was under the impression that the yelman on a kilij moved the pob further down the blade, but recently I heard that the material is simply compacted in the center, and does not affect the balance. Which is true?

Manouchehr, in his book, Arms and Armor from Iran: The Bronze Age to the End of the Qajar Peroid (Manouchehr Moshtagh Khorasani), gives POB. Comparing the wide-tipped "kilij" style swords with swords with slender shamshir blades, the POB of kilij-blade swords are not further out, for swords of about the same length. Indeed, it looks like their POB might be, on average, closer in. (I haven't checked to see if this is statistically significant. In any event, not much closer in.)

Why would one want to move the POB out? Yes, people say this about all sorts of swords that widen towards the tip, but it's a very two-dimensional view of a sword.