All domestic for the J-11 seems a bit to fast in the procedure of turning the licenese production of the Russian Su-27 to a domestic J-11. While the J-10 sounds more likely of turning fully domestic, as it needs just a couple of things to make it fully domestic. Possibly the radar, and the engine from the AL-31FN to the WS-10A
By domestic, it means made in China regardless of parts origin. The J-11 in PLA literature is also described as an all new domestic fighter even though it uses Russian supplied CKDs.
My personal opinion is that at this stage, the J-11B is ready to enter an initial operational status with one or two regiments, though its a stage behind the J-10 which has gone fully operational. If the J-11B goes IOC I would think the 1st Division is the most likely place being located in Shenyang and conveniently close to the factory. The 1st Division is the first unit to be completely J-11 (although the 2nd Division was the first unit to recieve some), and the first unit to get J-8F.
As you note there is some rivalry going on between Shenyang and Chengdu. To have J-10s in Shenyang's backyard can be regarded like an insult to Shenyang, and more so if the J-10 takes the regimental "0" lead number. This can demote the J-11s and the J-8F of the same division to "1" and "2" respectively, meaning secondary status.
You can see how Su-30MKK got demoted in the 3rd Division. The 3rd Division is the first unit to get the Su-30MKK and now the planes have gone from "0" to "1" in regimental status while the J-10s take "0". To add insult to injury, the pilot jacket badges of the units are now sporting a new design with a J-10silhouette on.