You're an Imperial Agent! You don't work for the Chiss Ascendency.
That was my basic reasoning behind accepting the mission. And the fact that the Empire and the Ascendancy would both be in more trouble without the other.
But your other analogy isn't quite accurate at least in this case. The Chiss are recent allies, not members of the Empire. No Chiss has grown up on an Imperial world, and they should (and would) still have their cultural and nationalistic leanings towards the Ascendancy, not the Empire as a whole.
Either way, if you're trying to keep something secret from the Chiss Ascendancy, why hire a Chiss to do it? Suppose I had been a bounty hunter instead of an Imperial Agent (it is an all-class quest, after all). Now, I have those same cultural and nationalistic leanings, but without the loyalty that comes with serving in Imperial Intelligence. There'd be a hypercom call to the Ascendancy 30 seconds after I broke orbit.