I can't agree that this is anything resembling the problem I was describing, though. That's the way the rules work and it doesn't violate the internal causality of the system. In fact, that's exactly what's happening on a smaller scale when someone declares a minority ARO, however, I'd leave it to @ijw to judge whether Exile ARO would fail in that case or if the now fireteam-less trooper might still be Isolated. Otherwise, congratulations on finding what is, I think, the second way of generating an Idle skill declaration due to requirements not being met when rolling. ...and it's not like Exile was guaranteed to begin with, so congratulations on having a Hack that breaks Fireteams with 100% chance instead of (without consulting the roller) around 35% chance (I can see a small issue with if your first declaration was something that generated a roll, but I still think all this breaking would do is cause the non-leader miniatures to not get to participate in a second Short Skill)
The primary effect of Exile is being able to Isolate things that you can't otherwise. That's what Hecaton is bitter about. Edit: thinking about this some, compare what would happen if you Exhiled someone who at the Final Coherency Check was found to be out of Coherency. Exile would go off without issue. Looking at the requirements for Exile. "The target must be an enemy trooper belonging to any kind of Fireteam." This was true when Exile was declared and at Resolution was true at a point during the order. So I see no reason why you wouldn't resolve Exile vs the target. So assuming the target fails it's BTS it would enter the Isolated state.