As to how the Sybil could play with our OOC decision I would expect any prediction she would to be volountarely open to conflicting interpretations, just like RL oracles where know to do. Her advice to the Kimaians is, in fact, a pretty good exemple of that: ''The people of Kimai will survive'' could both mean that the city will pull-it through or that the people will survive precisely because they would accept Eretria offer. If whatever interprétations peoples go with doesn't end up coming to pass the Oracle can always say the other one was right...
Look at it from a different angle:
Imagine the Sibyl, not as just a huckster, but as a woman trying to exert influence over the political landscape. What does saying "the people of Kymai will survive" do to affect the mindset of the city? Well, it focuses the mind on how to see to it that the people
DO survive. Which, when your city is threatened by a barbarian horde but the Eretrians are offering to carry the people away over the sea, may be a good thing for them to focus on.
Yes, it is a prediction that has multiple ways of coming true. But it has functions other than to be a "cold read" method for making the oracle seem prescient regardless of what happens.
Finally, I must admit that the whole argument that putting the Oracle in Nea Kimai will somehow get Greece itself to embrace the Divine Mariage a bit odd, to say the least. For one the Oracle was mainly popular in Italy and in Sicily, with only little cultural and religious pull in Greece itself, if any. Moreover, Eretria itself is both geographically closer to Greece and has more direct contact with it then Nea Kimai is likely to have so if the Oracle is to actually somehow pull that off its ods would be better in Eretria then in Nea Kimai.
Bear in mind that being 50-100 miles away across the Adriatic isn't actually really
closer to a given point in Greece than being 100-200 miles away along the coast of the Adriatic. With the crossing so hazardous, a lot of merchant traffic will deliberately avoid striking out directly across the ocean, or will take the very narrowest possible crossings. Most sailors would rather travel for several days while staying within a mile or two of the coast than spend even a single day out of sight of land.
Finally, on religion and augurs, bluntly, it's part of the quest. It's not an addition and I don't know why people keep saying that the Grand Mantis is obviously rigging things. I have said multiple times that the system is not being rigged, and in any case the Grand Mantis is a sortition position which gets switched out every four years. There are permanent priests and seers, but they don't have anywhere near the same power as they do in Ancient Rome where the Pontifex Maximus is a major position. In any case, it adds an element of randomness to elections, and forces players to consider things as people in the era, not ruthless maximizers. That the augurs allowed Demos Antipatria to blow open what was once the massive dominance of the Demos Drakonia isn't a bug, it's a feature, and it's also one that helps protect democracy so long as it remains neutral.
I think this bears amplifying a bit.
This ties into the point I made some weeks ago, and that others made more recently, about Roman battle tactics and how listening to auguries for tactical advice could actually make the Romans more effective in warfare, even though we today would conclude that they were basically determining their tactics via a random number generator. Specifically,
randomness can improve a system. Especially a system that contains few other procedural barriers to prevent failure of the system.
Greek democracy is very hit-or-miss when it comes to preventing single-party rule. Having a random element that can sometimes just (in effect) roll the dice and convince a large chunk of the electorate that it's Time To Change regardless of
why is a good way to disrupt this. If all political parties within the state are good-faith actors with reasonable ideas about how to proceed, it is probably for the best if power is shared between them- which makes things like sortition and rule by auguries useful, as a check against the natural tendency of people to become very loyal to a single faction or ideology.
If oracles are effectively random number generators, then this is no different.