In truth there is no such thing as a talking bird. They can mimic sounds that they hear, including human speech. Some birds are prolific mimickers and some will never repeat anything you say, no matter how many times you say it. I believe that most birds that mimic start when they are late juveniles or early adults, although there will always be some exceptions. I have met some gorgeous African Greys that were saying "hello" at 12 weeks old.
We have noticed that Eclectus Frankie and Jardine Jessie have started copying some of each other's sounds (Jardines in the wild are known to copy the sounds of other birds), although they haven't picked up any of the budgie noises. Jessie and I often whistle back and forth at each other. Frankie says "Ow!" a lot, which may be something to do with the noises my wife Yin makes, teaching him to step on/off arm and hand, or it could be something completely random that he has made up.