The Ascians in 2.1 (spoilers!)

[Alberel]

I'm starting to believe that the Ascians are beings from the Void, and that the Void is the world surrounding Zodiark, much like Eorzia is to Hydaelyn. Eldibus and Lahabreus summoned quite a few Voidsent in their respective story lines. Final Fantasy has had a history of the dual world, and the name drops of Krile and the Baldesians hints to such like was in FFV. Perhaps the Ascians are the ruling class of their world, with the Baldesians being a sort of resistance group.

The BLM quest line suggests that the Ascians are indeed a powerful form of voidsent. Weaker voidsent can cross over through gaps in the barrier between the two worlds but more powerful creatures cannot fit through and instead send their power (aether?) through to possess a host. The ascians too can only manifest by taking a host and their reliance on voidsent as minions does link them to the void.

I don't think his words elude to a specific previous agreement, but rather to the general concept that foreign emissaries (or ambassadors) are to be treated with respect. On earth, they often even get a form of legal immunity meaning they can't even be prosecuted for crimes. If he views himself as a representative of a foreign "state" (Zodiark) and we are representatives of the "state" he's visiting (Hydaelyn), than our drawing weapons on him would be a breech of standard diplomatic practices.

He says that Minfillia's forebears are to blame for not passing the knowledge on so I think it's correct to assume he was referring to a specific understanding of sorts between the civilizations of old and the Ascians and not just general etiquette.

@OP: With regards to the idea that becoming strong enough in the echo would allow the mortals and ascians to see eye-to-eye... I believe strength in the echo would allow us to see farther back into the past, presumably to the very beginning. It's becoming quite clear that something existed before Eorzea and Aldenard, something very different. The Ascians imply on several occasions that Hydaelyn tipped the balance and changed everything in some way and Zodiark labours to reverse the change and revert things to their original state. It may be that if the Warriors of Light develop enough strength in the echo to see back to this event they may not see the Ascians as enemies.