Let's take a look back through the history gamewise of the series. During the time of 1000 AD, Serge lived in a timeline he should have technically died in. Because of this a future where Lavos won was created, and from Lavos, it spawned chaos across the worlds manufacturing alternate split dimensions in every sector. Suddenly, time traveling was not as important as
dimension traveling. Because of this incident Crono and Co were stopped from succeeding in destroying Lavos during the events in Chrono Trigger. At the same
time it caused the Time Crash, which swallowed up their entire future in one world, and caused chaos in still another. The dimensional split however caused
by the Time Crash, triggered an alternate dimension which does not exist. The setting in which Radical Dreamers is played in, is that dimension. When the Time Crash occurred, a doppelganger of Serge was made in another reality not his own, one where Serge was a thief all his life, and grew up with Kid near the Zenan Mainland. At the same time, another doppelganger was created in the form of Lynx, whom owned a large spacious mansion which was totally different looking then the Viper Manor of today. However, the similiarities still paralleled eachother, things like General Viper, Lucca Ashtear, all of these
things were still set in stone. But the reality of Radical Dreamers was an event, created by the Time Crash, which never even happened. At the end of Chrono Cross when the Chrono Cross itself is used, it causes all of the dimensions and preceeding alternate parallel worlds to unify back into one continuous flow.