I'm not sure what you're getting at.
That said, it's likely that Jillian was "not performing a search" in the sense that she was simply going through the motions and not really trying to find the wounded dwagons. However, that's a distinction without a difference -- she'd still be on an unpredictable (except to a Predictamancer, perhaps) route for the first portion of her move that turn, and her route would have to at least superficially resemble a genuine search pattern (or else Webinar would have an excuse to reject her orders on the grounds that they conflicted with Ansom's).
(If anything, it would be more difficult to predict the route of a half-hearted pretense of a search than to predict the route of a legitimate attempt at an efficient search pattern.)
You mean where she declares that she is changing the mission ("So here's the mission now." (emphasis added))? That's exactly what Narkis said in the first place.