JCB uses their own exchange rate, see e.g. http://www.jcb.jp/rate/usd11172014.html

(Change the date in the URL to the transaction date.)

You can see that as of 11-17 ('recently') they were using $1 = 116 JPY (the 'mid' rate). Discover shouldn't manipulate that rate any further, so you may need to contact their CS for details. The Discover network doesn't support DCC, and if you're being charged in JPY at all, DCC/currency conversion wasn't done.