In regards to Lahabrea's commentary on Bahamut
We already have some in-game information that contradicts quite a bit of this, and some that can be easily read into to contradict it as well.
By that framework, all the Ascians would have to elementally match their Esper / Lucavi counterparts in Tactics / XII; we know this to not be the case. Nabriales would have to be associated with poison attacks, but he runs the gamut from earth to electric to time. Igeyorhm would have to use soul(?) based techniques; she relies on ice. Most damningly Lahabrea would have to use ice attacks, but he relies on its polar opposite of fire.
As for the Lesser Ascians, their name scheme is derived from their master's zodiac sign number and a suit of the Lesser Arcana. All of the Black Masks we have yet encountered were Lahabrea's underlings, with Lahabrea being associated with Mateus, the Corrupt and both of them the Pisces constellation. Pisces is the 12th (traditionally last) constellation in the Zodiac, leading to their number. Their "name," such as it is, is derived from the Lesser Arcana - Swords, Chalices, Staves, and Pentacles. Thus if the other Ascians were to have Black Mask underlings in Lahabrea's style, Pashtarot for instance would have his underlings named "Ascian of the Fourth [Minor Arcana]." Whether or not they can traverse the barriers between the planes and visit other Reflections is unknown (they probably cannot; unlike the Overlords the Black Masks do not have Dark Crystals and lack the power to possess a living host, forcing them to possess corpses to maintain their vaunted immortality), but their names are (probably) not derived from their Reflection of origin.
In regards to Lahabrea's commentary on Bahamut, it's likely they simply never expected to see the elder primal again. While the Ascians do often push and prod civilizations into Calamities / Rejoinings / Ardors / whatevers, van Darnus says that Project Meteor was his idea and his alone upon defeat. The Ascians were certainly indirectly responsible for the fall of Allag, but I can't say for sure whether or not they had any further plans for Dalamud (was Bahamut draining aether that whole time? Shouldn't the planet be dead if he were up there for five millennia? Or are primals not as inefficient as we've been led to believe? Could he drain aether in space? Christ, the questions!) and his release was just serendipitous or they intentionally prodded Garlemald and Nael specifically into Project Meteor.
We're not certain of the origin of the Ascians. My current hypothesis on the matter is that they were created with Zodiark's dying breath to resurrect Him ("For hate of the Star, to the Seas He cast His doom") and may be what the Twelve are actually based on. Maybe. Possibly.
I'm still not sure precisely what Nabriales meant when he said that Lahabrea and Elidibus were "of this world," but - and I apologize in advance if this comes off as abrasive - I don't think looking at the Ivalice mythos and overthinking it like this is going to give us the answers.