Fixing Direction Arrow problem

[Ref]

I was officiating grade school games yesterday. My first game there was a problem that I feel like we didn't correct in the right way. Last eleven seconds of a close game, players tied up the ball. I called jump ball and we went the direction the arrow was pointing.
About 6 seconds went by and we had a dead ball. The person doing the clock hit the buzzer and motioned for me and the other ref. He told us, he forgot to change the arrow, so it should be the other team's ball when I called jump ball.
I was wanting to let the clock remain the same and reward the team, which should of had it in the first place, with the ball. My partner said " No we will put approx. 6 secs. on the clock and reward the team with the ball." I felt this was wrong, but being he has more experience than my 2 years, we went his way.
With the coach arguing about his call, I felt we made the wrong call.
However, at the end it didn't matter. The team which got the reward of the ball, still lost by 3.
Was I right? Was my partner right? Were we both wrong?
Eddie