If it's AP1 and you have autopilot engaged, then when you hit the turn signal, it will change lanes. If you just have TACC engaged, and signal, then it won't auto change lanes as you're not in an auto steering mode with just TACC.
Now, there are some caveats. If it thinks there's an obstruction, like car ahead of you in the lane you're changing into and the following distance is too close, it won't change right away until there is sufficient separation. Also, if there is a solid white line, not a broken line, then it sees that solid white line as one it's not supposed to cross. Now there are cases where some road details, like say a solid black type of strip from say sealing cracks between lanes can be perceived as a solid line, and it won't change.
And yes, it does take some time before it will begin to change lanes.