Sounds correct to me. I've been going through alternating throw-in situations quite a bit over the last week and as long as it is legally touched inbounds like it is in this situation, arrow changes ball to B for AP throw-in.

Only instances where arrow is not switched that I have come up with are foul committed by either team and a kicked ball by B as the first touching.

Rule 4-42 and case book have helped me with this.