I see what you're saying. The best explanation would be to say that the Time Devourer can only "devour" one timeline. It lacks the power to cross over to separate timelines (where Serge defeated it) and devour them.
That isn't the case, because the Time Devourer is supposed to consume all space and time.
Belthasar: The Devourer of Time is a new life-form... Born out of the fusion of a life-form from this planet with Lavos, who nests on the far side of the dimensional void. In the far-off future, when the fusion ecomes complete, IT will awaken... Then, the Devourer of Time will begin to consume all space-time continua... Despair and hatred... To return all things to nothingness... That is what IT desires.
I'm not exactly sure I understand what you're saying and I'm not sure I communicated properly what I wanted to say. Lemme try again.
Even if the two timelines are perpendicular, at some point in the DBT the Time Devourer will face Serge, correct? At that point, whenever it happens, there is the possibility that Serge loses. If the Time Devourer is successful in any timeline, this would mean the destruction of the universe. Thus, if there exists a timeline for every possible outcome, the destruction of the universe would be inevitable - if the DBT follows the same rules as other timelines.
Does that make sense?
This isn't too hard to understand, but I explained it rather poorly. I'll try to be more sensible this time.
If the TD existed on the same space-time as Serge, in the time-line where Serge had not yet defeated the TD (i.e. before the time crash), the TD would have an unlimited duration of time to mature and thus result in the destruction of all existence. If the TD experienced a passage of time as time passed in normal space-time, the TD would have appeared and destroyed all existence the moment Crono landed the death-blow to Lavos.
Thus, we conclude that time does not pass relative to the outside universe for the Time Devourer in the Darkness Beyond Time (the time axis are perpendicular). This is similar to how Lavos' pocket dimension behaves: Lavos experiences a passage of time, but not relative to the outside world. From all time periods, Lavos appears to be in the same state. This is explained in more detail in the Lavos topic.
In Chrono Trigger, Lavos is always fully mature. In the original timeline, Lavos was mature because the Day of Lavos had occurred. We can conjecture that the Reptite Dimension would exist while Lavos was maturing within the pocket dimension. After Crono Started changing the time-line, Lavos remained unchanged, regardless of the time-period.
Likewise, the Time Devourer exists within the Darkness Beyond Time, which is a completely separate dimension from Home/Another. The TD experiences time as we know it, but not relative to Serge's space-time. At every instance on the TD's time-line in the DBT, it appears frozen in time from any point on Serge's time-line. An unlimited time may pass on Serge's time-line without the TD every appearing. The instant the TD reaches the maturity on its own time-line, it will instantaneously be manifested at all points on Serge's time-line—a scenario which never comes to pass. Even in the bad ending of Chrono Cross, the TD simply returns to its (relatively) frozen existence, and Serge may live out his life in peace.
All possible time-lines may be represented by separate dimensions. We don't know whether the DBT is common to all dimensions, or if there can thus be more than one TD. It would seem that if there are multiple Time Devourers, the destruction of the universe is a possibility. This is a topic requiring further discussion.
