Why do the Cults of the Dragon Below worship the Daelkyr and other abberations? Those creatures aren't the children of Khyber, they're invaders from Xoriat banished to Khyber by the Gatekeepers. Khyber's spawn are Demons, Devils, and the Rakshasha. Wouldn't Cults of the Dragon Below be demon worshippers, not Lovecraftian cultists?
While I can't speak for all the editions (I only have a fourth edition book), the cults of the Dragon Below are completely out of their rocker. There is no single unificating element amoung them other than they worship the beasties which are currently imprisoned in Khyber (as such, it's entirely possible that there are cults worshipping demons - especially in the Demon Wastes). Which is why the common folk call the cults that. However, the Rakshashas and their kin tend to hide in the shadows, operating behind the scenes. They have little use for a group of cultists who run around screaming their patron's name as they burn down villages (though they may, from time to time). If there are demon cults, they, like their masters, tend to be sneaky about it. Which means the cultists worshipping Lovecraftian thingies from Xoriat are more commenly encountered, colouring the public perception of the cults as a whole.
Keith Baker has also said that "Cult of the Dragon Below" is a mostly academic label and that few groups that would be commonly considered as such actually call themselves that. Daelkyr-worshippers, demon-worshippers, and those that worship Khyber itself as a divinity all get lumped together by outside observers.
As far as most people in the world probably know, the Daelkyr and aberrations are of the Dragon Below. Specifically, the Daelkyr in Eberron have been trapped in Khyber for something like 9,000 years, while humans have only been on Khorvaire for about 4,000 years. Nor were most of the other non-goblinoid races anywhere nearby when the Daelkyr wrecked the western continent. From the modern humanoid perspective, it's not really worth making the distinction because they've been a fixture of Khyber from beyond living memory.
Poorly Informed Extremists? Maybe we need a trope for that...