Tekken Tag Tournament is not a part of the Tekken canonical storyline. This allowed Namco to bring back the characters that did not appear in Tekken 3 (such as Baek Doo San, Bruce Irvin, Jun Kazama, Kunimitsu, and Michelle Chang). The ages of the characters in this game are the same as the ages that they had in the last game that they were in.
Because Tekken Tag Tournament is a non-canonical game, it has no story. It is more of a compilation of Tekken, Tekken 2, and Tekken 3, allowing players to use almost every character in the Tekken series. The only characters that did not return from previous games are the first King, Marshall Law, the first Jack robot, the first Kuma, Gon, and Doctor Boskonovitch (although Dr. Boskonovitch does make a cameo appearance in Tekken Bowl).
Tekken Tag Tournament also introduced two new characters, Tetsujin and Unknown. Tetsujin is a "pallette swap" for Mokujin. Unknown is the final boss of Tekken Tag Tournament. Both of these new characters are "mimic" characters. Tetsujin never returned to any game in the Tekken series, but Unknown returned - once again, non-canonical - Tekken Tag Tournament 2.