Chinese are buying RD-93s in huge number only because they will end up with Pakistan, uptill now there's been no official statement about engine on FC-20, The present form of WS-10 is in no way acceptable & if the horror story of WS-10 continued, PAF will have other option but AL-31 or may be delay induction of FC-20 :S
China has no plan to induct JF-17 for now, so almost all RD-93s will end up for PAF JF-17s plus I havent been to find anything reliable about WS-13, except that its serial production began in 2009.
October Surprises In Chinese Aerospace
Scroll down & read under heading
'New Engines'