The answer is "No", the official was not correct in calling it a backcourt violation. There was a long discussion about this question in an informal group session of veteran officials on the test.
Even though the deflected ball still had frontcourt status when it was caught in the air by A-2 in the backcourt, A-2 was not next player to touch the ball after A-1 or any offensive player touched it. Since it was B-1 who last touched the ball in the frontcourt, a backcourt violation cannot be considered here regardless of the ball's frontcourt location status.
Here's an example to illustrate this: Suppose A-2 is still in backcourt as A-1 dribbles the ball over the division line and achieves frontcourt status. Suddenly, B-1 deflects A-1's pass to A-3. The ball bounces high off the frontcourt towards the backcourt. A-2, who never reached the frontcourt because he/she is lagging behind the play in backcourt, sees the ball coming toward him/her in the air as a result of B-1's deflection and catches it. Is this backcourt violation? I think not. The question is similar in this respect, since A-2 had already achieved backcourt status before the ball was caught in air in backcourt. The only difference between my scenario and the question's scenario is that B-2 ran from frontcourt to backcourt to catch the ball off the air. Nevertheless, in both cases, A-2 has backcourt status.
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