From what I understand, Minseok definitely was part of the Masters program for a Music major in "Applied Music" at Catholic Kwandong University back in 2014 and we even have a presentation he gave back then which was recorded, see below. There were statements from professors as well so it's well supported.
https://xiuminindo.wordpress.com/2014/11/27/trans-audio-141126-xiumins-presentation-at-gwandong-university/
https://xiuminindo.wordpress.com/2014/11/26/compilation-141126-xiumins-presentation-at-catholic-kwandong-universitys-applied-music-seminar/

However, the evidence that he did a PhD is spottier, even in part is more spotty and what exists is present in this Koreaboo article (https://www.koreaboo.com/stories/exos-xiumin-is-pursuing-his-phd-at-hoseo-university/). Essentially these reports were based on a visit to Hoseo University by Xiumin as well as a person claiming on twitter that he was currently completing his PhD program and that it was not in contemporary/practical music. As far as I'm aware, we never got any other information on the subject making it difficult to know if this is true but if anyone knows anymore, please speak up in the comments!

Hope this helps!