@puzzlezaddictFinally!!! I solved it! I started what you suggested first! It worked! So..I started bringing over the previously made DCCache and DCBackup has only hair and clothing store sets excluded premium contents. After that, I redownloaded the multi tab from sims3.com, and it worked. I tested this with Christopher Steel in Sunset Valley with NO CCs and mods. I added all premium contents and worlds I own, and it still worked too.
Finally I started adding mods and everything worked perfectly. I started adding CCs in Mods folder, then multi tab stopped working. I didn't know CC would be affect to the premium contents. A couple of months ago, I found SimsVille custom world includes a bunch of cc files in it. It was made for the sims3 simmers who is missing the sims 1. One of the CC items was causing this issue. The file name is 'cloned_basketball_hoop.package'. For the last test, I removed all mods and ccs from Mods folder, and put this item only into Mods folder. Christopher couldn't listen to tabcast. Finally, I opened my own sims 3 folder which has my real sim family save file. I only removed this cc from Mods folder, my sim family is able to use multi tab properly. Thanks!! But I still have no clue why the frio brothers couldn't make it work without Mods folder.
So I guess it could be from the 2 reasons. One is from the broken ccmerged file as I tested it just before removing old DCCAche and DCBackup folder. The other one is from this CC content I guess. Anyway Thanks a lot. 🙂 You gave me a key for solution.