Interesting resumption from a kicked call

[Damian]

After calling two games, I watch the 3 man crew do their mechanics.

At the begining of the second qtr, White should have gotten the ball. The refs, the players, and everyone got into their halfcourt positions. But, the blue team came to perform the throw in. None of the refs, coaches, players, or the very vocal parents noticed this and gave them the ball. They immediately took it the other way for a layup (missed).

What really surprised me was that they then had the possession arrow point to blue. They said that since it was pointing to white, then the next one should point to blue. I was thinking the term Possession arrow meant possession and the arrow should have stayed pointin towards white. What would you have done?