So Janus was sucked by the Time Gate like if Crono wasn't been there? I had asked this because in the "second" disaster he wasn't in the room of the Mammon Machine... Or at least we don't see him.
Err...sort of.
Basically, Time Bastard is the theory that any new altered past self produced as a result of having one's own past changed---while one is a time traveler--will disappear and be replaced by the older self at the time of time travel. (Please note this is extremely simplified and the full theory is present here on the Compendium.)
To put this in perspective, let's take Janus' situation. In the Lavos timeline, he was present during the Ocean Palace Incident and was sent forward through time in to the era of the Middle Ages, where he grew up and became Magus. As Magus he was killed by Lavos when he summoned Lavos to his castle in 600 A.D.
In the new timeline created by Crono and friend's interference, Magus is sent back to 12,000 B.C. anywhere from a few months to a few days before the Ocean Palace incident--I like to think about two weeks is the amount of time--and became the Prophet, using his future knowledge to his advantage to try and defeat Lavos. The Gurus were imprisoned or banished and thus would not have been present. In this timeline, he would have been killed by Lavos during the new Ocean Palace Incident created by this altered timeline.
Now we take the timeline where Crono and friends appeared and interefered even more, the new Ocean Palace Incident as we have come to know it. In this instance, Magus survives through the good graces of Crono and friends, as well as his sister.
In this same timeline, Janus--Magus' younger self--occompanied Schala to the Village of Algetty, because she had heard Melchior had been freed and wanted to ask Crono and friends to stop her mother. (Remember that previously this would not happen as Melchior would remain on Mount Woe through the Ocean Palace Incident in the instance where Magus is the Prophet without Crono interfering.) Because Janus occampanied Schala, he then remained on the mainland with Melchior afterwards, as we know from the Elder of Algetty/Last Village.
Thus, he was never able to be present at the Ocean Palace Incident, and yet the Elder of Algetty reports that both Melchior and Janus disappeared into a "black portal."
We know the personal histories of Melchior and Magus do not actually change. He still reports the original Ocean Palace Incident in his memories to Crono's friends. Melchior does not disappear from 1000 A.D.
Therefore, what happened with Janus and Melchior? That black portal, as I said before, is taken by some--including myself--as an example of Time Bastard in action. The new versions of Melchior and Janus created through Crono's interference simply disappeared, replaced by the original version of both appearing when they did in the first timeline.
Hopefully this all makes sense. I recommend you read this article if it doesn't however, as it goes far more in depth on everything and should make everything clear:
http://www.chronocompendium.com/Term/Principles_of_Time_and_Dimensional_Travel.html