Time Traveller's Immunity states that travellers through time are immune to actions that would alter their own existences. This has constantly been a theory used to explain why instances where the Chrono crew's lives depended on their own actions in the past, they would remain unaffected by their lack of action or progress.
This theory has been clashed by one major plot point in the game, Marle's disappearance from the timeline in 600 A.D., referred to as the "Marle Paradox."
Two items that support TTI, are Magus' interventions in his own past, and Melchior's unaltered future during Magus' interventions, and meeting the Chrono crew.
To explain the latter, minus TTI, I put it that the changes made in history by Magus and the others did in fact change Melchior in the present, however at no point in the meddling done was his position there neutralized.
This is because the nature of Melchior and the other Guru's travel from 12,000 BC to their respective time periods was not in relation to their proximity to Lavos.
The Entity began affecting time in an effort to protect itself (The Planet) from destruction at the hands of Lavos. Naturally this would require it to protect the lives of those who would play an integral part in achieving this goal. The gurus each played such a role, thus it was the Entity, not Lavos, who originally and still in the altered timeline sent them through time at the moment of Zeal's destruction. This is supported by the statement that the Earthbound ones saw Melchior and Janus pulled into black portals after the Ocean Palace incident (The same black portals found during Magus' flashback to Ocean Palace). When Melchior was imprisoned on Mt. Woe, I theorize that the Entity still pulled him from his prison through time, to preserve this same outcome, regardless if Crono and the rest rescued him or not.
As to why Melchior never makes mention of recognizing Crono and the others, I believe this is because he realized upon seeing Crono in the Millennial Fair that he too was sent through time, and felt that he may play an important role in time. With this knowledge, rather than react to Crono with recognition, he feigned ignorance and behaved as if he were meeting him for the first time, in order to preserve the newly forged past he found himself with.
Explaining Magus' past being affected by his own actions is a different story. While the actions he took would indeed change his current self, the memories of the lost timeline destroyed by his actions remained. This would actually carry support for Zeality's theory of lost memories not dissappearing into the Darkness Beyond Time entirely, but rather channelling into the most similar incarnation of that memory, or dreams as he put it.
Link Here.This would explain how Magus could still recall the original history of the Ocean Palace incident, and recite it for the Chrono crew. As with Melchior, his own existence (Janus' future) was never altered during his meddling, as the Entity was always ready to ensure his time travel at the moment of Lavos' emergence.
Any arguments to this?