Posession Arrow Change after T?

[ranjo]

Boys AAU this past weekend. Visitors assistant coach is acessed a technical foul at halftime for continuing to argue a call after the half is over. Home team has the arrow. We shoot the technical to begin the second half and give the ball to the home team at the division line for the throw-in. As the ball is thrown in, I notice the table has turned the arrow and it is now pointing toward the visitors.

I don't think the arrow should have changed, but trying to referee, run, chew gum, and reason all at the same time is too much of a challenge for my old brain.

Was I correct that the arrow should not have changed? I now think the throw-in was the result of a technical foul penalty and not an alternating posession.