This will be my first post here but I have read various threads and articles on the Compendium for a few years. I am finding some issues with the theory of TTI as it relates to the Ocean Palace incident in the Keystone timelines. As you know, in the Lavos timeline, absent of any action by the Crono team, Janus and the three Guru's are shipped into the future during the Ocean Palace disaster. They show up in their respective era's, simple.
As the Crono team continue to travel through time they eventually challenge Magus and win, interrupting his summon spell for Lavos, sending the Crono team to 65M BC and Magus to 12,000 BC. (maybe slightly earlier but it is irrelevant) The important piece of info is that Magus appears from the time gate before the Ocean Palace incident.
Magus, posing as a prophet, convinces Queen Zeal to dispose of the 3 gurus. (Melchior is on Mt. Woe obviously, though there is no concrete evidence of the whereabouts of Belthasar or Gaspar)
Since the gurus are not present in the Ocean Palace, they are not sent into the future. Janus may or may not be there since he is not detained but it is irrelevant because the Magus that is sent back to 12,000 BC will emerge from the gate no matter what happens to the Janus from that point on.
I don't believe that TTI applies to the Guru's since they are traveling into the future from a point in a time line that no longer exists. If they are prevented from traveling into the future because of a time traveler other than themselves, (Magus) then they will not emerge from the gates in the new time line.
*** It is debatable whether Janus even would emerge in 5** AD. If he did, it would be because he was sent there in the new Ocean Palace incident (before Crono team interfered but after Magus arrived in 12,000 BC and had the guru's detained). That Janus WOULD show up in 600 AD and likely have lived nearly identical to the way Magus did, but when summoning Lavos and being interrupted by the Crono team would vanish into the DBT, likely along with that version of the Crono team so that Magus could appear in 12,000 BC. If he did not appear in 5**AD he was not in the Ocean Palace incident. Then, in 600 AD, the world would have been completely different. Cyrus would be alive, Glenn would not be Frog, even though Frog would still emerge from the gate in 65M BC with the Crono team because of TTI, and Guardia would have likely had much less wartime hardship from the Mystics.
Back to the Gurus. When Crono team initially warps to 12,000 BC from 65M BC to a point after Magus arrives they are banished from the age via Schala's seal on the gate. When they travelled into the future of the newer time line there would be no Belthasar, and consequently, no Epoch. Melchior would not exist in the new time line in 1000 AD but is irrelevant to the Epoch part of the quest. Gaspar MAY be at the End of Time since that is not part of any particular time line and time runs perpendicular to the time lines.
I do have a theory of how the Guru's WOULD appear regardless of changes to a time line based upon pocket dimension theory. Since they are gated away during the original Ocean Palace Incident while inside Lavos's pocket dimension, and since that pocket dimension exists for all time that Lavos does on the planet, perhaps they are simply exiting the pocket dimension at specific points in time, regardless of the time line. The only problem lies beyond the game of Chrono Trigger and into Chrono Cross. After Lavos is defeated by the Crono Team in 1999, Lavos and his pocket dimension cease to exist after that point in time so Belthasar would not appear in 2300, so no Chronopolis, no time crash, no Neo-Epoch, ect.
I look forward to input from anyone who wishes to give it.