I don't know when it will be done but it really doesn't impact your stay at all. The area under construction is shielded by attractive walls decorated with Tiki masks. The shops and Captain Cooks are open. I wouldn't worry about it at all.
Oh, and it did start before January. We were there in October and at that time work was going on in the back area where the children's clothing shop had been recently. It is now in the lobby to the side where the restrooms were. Without checking Tikiman's site, perhaps his latest pictures or reports were from January.