Calm down shorty....
Okay, here we go... Time Compression was the attempted and failed achievement of the "Everlasting Moment".
Ultimecia was attempting to compress moments of the past to the present she resided in (ergo the "future" that most of you cling to) in order to find that moment that she would no longer be persecuted. (cue music to "One Moment In Time).
Essentially, she could only compress moments of the past, NOT the future because that was what she was trying to avoid. What sense would it make to include the moment of her defeat and demise? Hence she sought out Rinoa and Ellone so that she could gain access further back in time past Adel's rule and Sorceresses preceeding her. I find it strange and oddly convienant, that era of Rinoa was as far as she could go. But also, it's possibly because Sorceress Edea was her Successor that she was able or only able to access this time period.
Anyway, the Sorceresses that the Fated Children were destroying while HITCHING a ride through Time Compression were the very Sorceresses that Ultimecia was seeking in order to aquire their power to ultimately achieve Time Compression. With each Sorcersses the Fated Children slew Ultimecia OR Rinoa absorbed these fragments of Sorceress Power.
My explaniation of Time Compression goes as such...
Let's look at this like "Dominoes" all set up ready to be knocked over in succession...
I I I I I I I....
Now as time goes each on of these dominoes or 'events in time' will fall over in succession connecting or 'knocking over' the next series of events...
I I I I\\\\\\
Understand.
Ultimecia, probably somehow knowledgeable of the fated prophecy set by the Fated Children knew that she was the Final Sorceress and did not want to die...
I(Ultimecia's Death) I I - (attemp with Time Compression)- I I I \\\\\
Let me know if I'm not explaining this clearly enough.
The fact of the matter is, is that time is immutable. You can not change it. This is why she sought to not so much as change time but to escape it in the moment between an event in time.
And here leaves the questions... If all the Sorceresses that were defeated where the Sorcersses of the past... Where is Rinoa's successor? Exactly, there isn't one. It is possible that Rinoa will eventually become Ultimecia...