I am not sure if the J-11 fighters were scrambled for that purpose. Around the time the cruiser was going through the Straits, the Chinese and Russians doing a joint aerial drill where Russia sent Tu-94 Bears and an A-50 down the Tsushima Straits, and China sent some H-6 and possibly an KJ-2000 to meet them. South Korean and Japanese fighters responded to intercept these bombers and there is currently some tit and tat going on with Russia and South Korea about why Russian bombers are flying over disputed Dokdo. The J-11s were probably meant to accompany the H-6s which is the usual pattern with these flights over the seas.