So, if I understood all well, Time Bastard and TTI theories say this :
Let's take Crono.
If Crono departs from 1000AD to go to 600AD, he creates a new timeline.
In this new timeline, a new version of himself, a Time Bastard, will grow up and will finally disappear when his personnal age will reach the age of the original Crono when this one traveled in the past.
Indeed, it's said in the Compendium that the disappearance of a Time Bastard is based on his/her/its personnal time (espacially for Kid's pendant).
Thanks to this, we can imagine a scenario in which a Time Bastard travels to the future.
In our example, let's say that Crono traveled from 1000AD to 600AD when he was 18. So that, his Time Bastard will live in the new timeline during 18 years before he fataly disappears. But it's not impossible that this Time Bastard, when he is only 16, travels through time as well !!
If he goes in the future : OK ! I will live here during 2 years and then disappear...
But now, what happens if this Time Bastard, before he dissapears, travels in the past and change history ?
Let's say that the Time Bastard of Crono, before his disappearance, travels to 300 AD !
What happens to him ?
And what happens to the original Crono supposed to arrive later in 600AD due to Time Traveler's Immunity ??