Soemthing to keep in mind, though: Chillborn only have Resist 10 Cold. So, if you have 3 with overlapping auras, that's 15 damage - the chillborn are going to take damage from one another's aura. So don't overlap too much.
So it looks like my DM is right by RAW, but it seems that the RAW is poorly written.
My only concern is that this stacking aura + extra damage effectively took our Warden out of the fight, since she only had melee powers. The rest of us all had main or back-up ranged abilities. It definitely increased the amount of unfun for the Warden's player...
Thanks for the replies, all!
I don't think that's how it would work.
3 chillborn zombies wouldn't have an aura that deals 15 damage. They would have three auras that deal 5 damage each. Since they're separate instances of cold damage, they would resist each one separately. No matter how many chillborn zombies you have, they could never get past Resist 5 cold (barring possible immobilized creatures taking 10, in which case, replace Resist 5 with Resist 10).
It specifically uses the wording that the auras are cumulative.. that suggests that the damage is actually together.
I'm not convinced that "cumulative" means "add them all together and apply them once".
My personal interpretation would be that it means "you take this damage from each chillborn whose aura reaches you". In other words, 3 chillborn do three lots of 5 damage, rather than just one.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.