I'd say the Ith have very much misunderstood the Empire with their demands. I'm quite certain they think the hit was actually a serious blow, rather than mostly just pissing people off. They probably also misunderstood how the demand would be taken, though I'm less certain. Misunderstandings and the problems thereof are kind of a running theme for the quest, you know?
Look at how the thing with the polar nation went. There was plenty of incomprehension there, and that was two groups who wanted to understand each other, and had some connection to start from. I won't say the Ith are more different than the Polar Nations, because we don't understand them and I suspect they are more similar than we suspect, but they are definitely less well placed for understanding.
Now, I've seen the argument brought forth that they should know better, because they have human traitors working for them. But that requires listening and believing them. This is quite rare, because if you're a xenophobic warmongerer who thinks the opponents are lesser, why would you make an exception for those guys? Further, those guys are traitors, and therefore by definition not trustworthy. Especially for a highly communal society like the Ith. Do you really want to discuss deep strategy with them, or base it on their opinions? Really, either the enemies do things the proper and reasonable way, your way, and you know how they will act, or they will act as stupid fools, in which case they'll lose and don't require much consideration.
And honestly, they'd be right not to trust their human collaborators. They'd either be the outcasts who really despise the system (like Yan Renshu) or the sociopathic and ambitious, who have a really low opinion on everyone else (also like Yan Renshu). Under the Hui, the outcasts could be pretty reasonable people, but with the Cai they'd mostly (mostly!) be people who are outcasts for a reason (like Yan Renshu).
Do you expect good advice from Yan Renshu? Gods no. He's so myopic, self-centred and disdainful of everyone else that he couldn't give you good advice if he wanted, and also so myopic, self-centred and disdainful of everyone else that he wouldn't want to. You couldn't even get a clear idea of culture and expected reactions, because he's so wrapped up in his worldview and persecution complex. I'd be like trying to understand the american legal system by talking to a sovereign citizen.
At most, I expect they came up with a strategy in line with their normal operations, and then asked Yan Renshu and his ilk for comments. Now, if you've placed yourself in the grasp of an alien society at war with your home nation, and they ask you if their plan is stupid, are you going to tell then yes? Seems a bit risky, doesn't it? Maybe you'd just try to nudge them in a better direction, but not say so directly. Yan Renshu certainly wouldn't. Although, I'm not convinced he'd actually think it's stupid. He's extremely callous, and also thinks everyone else is weak (in part because they aren't callous), and surely a demonstration of power would cow those sentimental fools.
And also, I'm not sure he actually knows all that much about how the empire works. Not really. He's from a merchant family which has conistently failed to reach the low nobility. He's not LQ. He's never been face to face with a White, he doesn't hang out with ducal heirs and the youth of the general high nobility, he hasn't met a dozen high ranking spirits and talked with them. He didn't get adopted by a winter spirit, or dance with the moon, or flitter as a burning spark between the clash of sovereigns. He got his worms from somewhere, but that's probably about it, and it wouldn't tell him so much about the higher ends of imperial society. He might know you become less flexible as you grow in power, but I doubt he understands. His perspective is mostly a mortal one.
And I suspect that other informants would be similar. The higher you go in the hierarchy, the more you have to lose, and the less viable going to the Ith becomes in the first place. It's not impossible for there to be those who'd risk it anyway. But it seems like the Cai rebellion would've cleaned out the vast, vast majority of them. They'd have a very easy time if the Hui were still in power, or with a place like the Celestial Peaks. Thousand Lakes too, before Sun took the discontent away (although the geography there is not favorable).
In conclusion: This is not a 4d chess move. It's a genuine fuck-up, because cross cultural understanding is hard if you're trying, and they're probably not.