Teams try to trade up in the draft so they can take a specific player, not just to have a higher pick for the same of having a higher pick.
There was plenty of talk from credible reporters about the Celtics trying to move up for every pick up until Winslow was picked. There were no rumors of the Celtics trying to trade up for one of the slots after Winslow was picked. The most likely explanation for this is that Ainge wanted to draft Winslow.
Afterwards, it was reported that the Celtics entertained the idea of trying to trade down but were worried that Rozier wouldn't be available past the Rockets at 18.