This is the change that was made to fix the Turner trade: "Major League Baseball emailed all 30 teams today to announce that, effective following this year’s draft, players selected in the amateur draft will be permitted to be traded beginning the day after the conclusion of the World Series." (https://www.mlbtraderumors.com/2015...eligible-to-be-traded-after-world-series.html)
There has to be something in place, or else there would be an easy work around for teams to trade draft picks. They'd just do like the NBA does and draft for each other, then make trades immediately when the draft ends.