Soo I just looked up https://twitter.com/ObamaFoundation/ up to december 2019 and they never posted a direct link to Obama.org
First time on May 17
This concludes, for me, that they used the "Celebrating the class of 2020" as hook to then send their message to all those students a few days later.
Same for https://twitter.com/BarackObama, first time he posted a link to his own website was june 1