He received his higher education at the Kharkiv State Academy of Physical Culture in 1985.

From 1987 to 89 Svystun made sixty one appearance and scored ten goals for Shakhtar Donetsk.

During the next four years Svystun played for First and Second League clubs Diósgyőri VTK and Nyíregyháza Spartacus.

During the first half of the 1998–99 season he played five matches on loan to Kremin Kremenchuk and scored one goal.

After he was replaced with Serhiy Yashchenko in 2015, Svystun remained in the club as an assistant.