We are taught that fly balls are the PU's call (*).
If so, then the BU should not signal anything.
However, if indeed there was confusion, we are also taught that you should rectify the mess you made, to the best of your ability.
IMO, your final call was more than reasonable. Had you called it no catch right away, it's not clear at all that the defense would have made the complete double play.
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(*) Notice that you did not call an infield fly in this case (makes sense as diving for the ball is certainly not "ordinary effort").
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