So have Bungie just forgotten that the House of Exile were made up of the malcontents from other Fallen Houses over the centuries of their presence in Sol? They are now being described as arriving in Sol during the Dark Age after fleeing Riis which is completely false.
I know there is time shenanigans going on in this expansion but I don’t think this can be explained away by that. They are also led by an Archon which goes completely against their principles in D1.
Bugs me that Bungie could have created a new house for this or simply said that they are a splinter of House Salvation or Dusk. Instead they break the lore for seemingly no reason, not like House Exile being present thickens the plot.
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They could be an "original" House of Exiles that formed during the Drift and wound up on Kepler. The House we're familiar with was formed from malcontents of the other Houses in the Solar System. After all, the Developer Insights revealed these Eliksni chose not to invade Earth alongside the other Houses to try and reclaim the Traveler. Not wanting to reclaim the Traveler and just find a new home could be grounds for a lot of these Eliksni to have been exiled from their original Houses.