Rather than logging in through the "Off-Campus Access" page first then pointing your web browser to DBpia, try accessing the database directly through a proxy link. You will find proxy links to DBpia on our library catalog (first link below) and Korean studies research guide page (second link below). If you are off-campus (and have not logged in previously for other services), you will be automatically redirected to a proxy server with two factor authentication using your WUSTL Key
After you successfully log in, you will be redirected to the top page of DBpia, logged in as a WU institutional user.
http://catalog.wustl.edu:80/record=b4206673~S2
http://libguides.wustl.edu/c.php?g=47242&p=303217
This likely has something to do with the way DBpia handles browser sessions. DBpia does not recognize WUSTL Key authentication done elsewhere, even within one browser session. It has to be directly handed off from the proxy server.