You were right in that arrow should have been set to team A. Although A1 did grab the ball, which could be thought of as possession, it was ruled a violation. Team B inbounds after the violation, setting the arrow to team A when the throw-in is completed. Sorry I do not have case book for citation.
A1 can legally be the first to touch the ball after the jump ball has ended when it has touched another player or the floor.
See this older but very similar thread where Nevada sets it straight:
Jump Ball