Odine is egotistical and assumes Ultimecia is using his machine, however we don't know this.
Exactly Odine only ASSUMES how Ultimecia can exist in present,however his assumption is wrong.Just read Rev of the Truth thread to more detail.
http://www.gamefaqs.com/console/psx/game/197343.html

ie. where the other FAQ you read is.
That FAQ is failed to explain TC.The explanation about TC in that FAQ is wrong,so just read "Revelation of Time Compression" thread.