I don't remember anything in Final Wars specifying Zilla's origin. It was just a random kaiju that was there for 30 seconds as a dig at the American film, nothing more than that. Yes, it was one of the kaiju unleashed by the aliens, so I can see where one could assume it had an alien origin, but the film didn't spell it out. It was too much of a throwaway for that. (Indeed, that was one of Final Wars' many problems. Most of Godzilla's battles with classic kaiju were just brief cameos, lip service to the history of the franchise as a half-hearted way of meeting the film's 50th-anniversary mandate.)
Also, a lot of people get confused about this, but Zilla in Final Wars was not meant to be the same creature from the Emmerich movie, just a lookalike. It wasn't supposed to be in continuity with that film; it was just borrowing a creature design from it. Indeed, the Tri-Star film can't possibly take place in the Final Wars universe, because FW is in a reality where kaiju attacks have been a worldwide reality for half a century.
It's worth remembering that the six Millennium-era films made from 1999-2004 were set in five distinct continuities, with nothing in common except that they were all sequels to the '54 original (except maybe for the '99 film, which doesn't explicitly reference it). So Final Wars is in a separate reality from GMK. As I mentioned, GMK is a reality in which Godzilla attacked once in 1954 and was not seen again until 2001. And it's the GMK reality that I consider reconcilable with the Tri-Star film.
Toho's original plan was to let Tri-Star do a trilogy of Godzilla films, then restart the Japanese series with a 50th-anniversary film in 2004. Since the Emmerich film failed, Toho rushed a new series into production. That's why the Millennium films are set in so many different continuities -- since they didn't have time to settle on a new direction for the series, they used the first three films as tryouts for various possibilities. The makers of the second film were the "winners," but instead of continuing its universe, they then created another new one which ran for two films; but then the series was cancelled due to low box office, so Toho finished it off with yet another new continuity for Final Wars.
So if Emmerich's Godzilla had been a success, we wouldn't have gotten the Millennium films at all. Instead, we would've gotten an entirely different Godzilla movie in 2004, one that was the start of a new series.
Also, a lot of people get confused about this, but Zilla in Final Wars was not meant to be the same creature from the Emmerich movie, just a lookalike. It wasn't supposed to be in continuity with that film; it was just borrowing a creature design from it. Indeed, the Tri-Star film can't possibly take place in the Final Wars universe, because FW is in a reality where kaiju attacks have been a worldwide reality for half a century.
It's worth remembering that the six Millennium-era films made from 1999-2004 were set in five distinct continuities, with nothing in common except that they were all sequels to the '54 original (except maybe for the '99 film, which doesn't explicitly reference it). So Final Wars is in a separate reality from GMK. As I mentioned, GMK is a reality in which Godzilla attacked once in 1954 and was not seen again until 2001. And it's the GMK reality that I consider reconcilable with the Tri-Star film.
And what would have happened had Emmerich's Godzilla been as popular as old Godzilla? Would it still have been punked by the so-called "true" or "real" Godzilla in that fanboy slugfest?
Toho's original plan was to let Tri-Star do a trilogy of Godzilla films, then restart the Japanese series with a 50th-anniversary film in 2004. Since the Emmerich film failed, Toho rushed a new series into production. That's why the Millennium films are set in so many different continuities -- since they didn't have time to settle on a new direction for the series, they used the first three films as tryouts for various possibilities. The makers of the second film were the "winners," but instead of continuing its universe, they then created another new one which ran for two films; but then the series was cancelled due to low box office, so Toho finished it off with yet another new continuity for Final Wars.
So if Emmerich's Godzilla had been a success, we wouldn't have gotten the Millennium films at all. Instead, we would've gotten an entirely different Godzilla movie in 2004, one that was the start of a new series.