Outstretched arms is not a fair catch signal.
If the kick returner who fields the ball plans to not be returning the ball and would like the coverage team to not touch him, he signals for a fair catch.
Illinois got caught with their pants down, full stop. Outstretched arms means nothing, absolutely nothing to a coverage team. If a coach is telling his coverage team to let up cause of outstretched arms, that's on him because that signal means absolutely nothing.
Even if a KR man signals a fair catch, the coverage team should be hustling their butts hoping for a muff. If you'd hustle your butt on a fair catch signal, why in the world would you let up on a signal that actually doesn't mean a thing to the coverage team?
Carolina noticed that Illinois was letting up once they saw outstretched arms, and they attempted to take advantage of it. That's what any good ST coach should be doing.