I never saw that bit.
What I think that happened was that the Pocket Dimension was parallel to the DBT, which caused Lavos to be transtimentional. As Lavos was destroyed, his energy that powered the pocket dimension weakened and it started coming apart. Lavos was sucked into the DBT and the end of him.
BTW, the moment Lavos is defeated doesn't cause a new timeline, it just changes the future. It's when Crono and co get back that the timeline is fully developed, but you usually say it's "instant" Sentenal.
Anyway, what I dug up from the game script (and this makes Starx on GameFAQs wrong about Lavos being psychic). Lavos was beaconed by the Flame and pulled back Chronopolis further in time than it should have. The idea was that the Lavos in 12,000BC saw Chronopolis and understood what was going on - that a group of time travellors would defeat him in the future. That Lavos would safeguard itself, which would cause the Lavos in the DBT to comeback.
By the way, I just had a thought. It wouldn't be too farfetched if Crono and co defeated Lavos in the Black Omen in 12,000BC. If it is not destroyed, the Black Omen would still exist into the future, and Chronopolis would definetely know that Zeal existed. Chronopolis actually does not have hard evidence that Zeal existed, nor that Lavos actually appeared in 1999AD in their time, and that it only happened in other timelines.
Basically, if Lavos was defeated in 12,000BC, then he truely would be out of time forever, even in 1999AD. And this may be why Lavos had to pull back Chronopolis so it'd interfer and Lavos would realise what was about to happen.