A lot of the confusion on this rule has to do with the definition of team control. B1 batting the ball does not establish team control for team B in the same manner that if team B had team control, the ball deflecting off A1 would not establish team control for team A.
A team can only lose team control if: the other team gains it, there is a try or tap or there is a dead ball. If you have team control, the only way the other team can "take it from you" (or if there is no team control, the only way they can establish it) is if one of their players gains player control. Player control is defined as a player "holding or dribbling a live ball inbounds". Therefore, a bat or a deflection does not establish player control, so a bat or deflection cannot establish (or take) team control.
That's part of why your case is a violation. Team A was always in control despite the bat by B1.
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