Travel or BC and whose call?

[Nevadaref]

You are correct that according to the strictest reading of the rules this is a backcourt violation, since the player secured control of the ball in the frontcourt, was not airborne, and then touched the backcourt.
However, I would not call it.
Was it a travel? Who knows? If the player did attempt to get up (whatever that means) then yes.
Who should call it? That depends on where the officials were when the play happened. If there were many players in the backcourt and you were near the division line to help with the press, then probably that is your call. If there were only a couple of players in the backcourt and the trail had come up to almost the division line while the lead was well down the court, then clearly the trail calls this. If both of you were close, I have no problem with a double whistle.
I will say that you two were fortunate that you each had a violation and on the same team. It is always a good idea to NOT give a preliminary signal on a double whistle, until you check with your partner! One of you may have called a foul or granted a time-out.