What can happen, and does at my school anyway, is that the school buys the Catholic Trials and thus commits themselves to using the CSSA timetable but.... they then allow the teachers to set their own papers. They may use the CSSA paper, the Independent, the ARC, Neap or a totally individually set paper.
For instance, I looked at the Catholic Trial for Modern and didn't like it for my students, particularly the personalities question as we haven't finished Leni properly yet so I decided to set a separate paper but the students still did it on the day set for the Catholic Trial. I will give them the Catholic one when they return to class on the 24th August.
If the CSSA timetable doesn't completely suit your school e.g. clashes in exams that mean students doing two exams at the same time one subject may be asked not to use the CSSA exam so that the timetable can be adjusted to suit the needs of the individual school. e.g. there would be students attempting both Extension 2 Maths and EXtension History and both their exams are on at the same time. The school has options - do what they do at the HSC - namely have the student do one in the morning and the other in the afternoon but be supervised in between exams or could choose to move one but not use the CSSA paper.
That is what has happens at my place, particularly this year as the Drama kids actually have their HSC practical presentation on the 20th August so the timetable would have to be adjusted with regard to the Music exams to suit any kids who do both Drama and Music. I don't know if anyone actually is doing both subjects this year but I wouldn't be surprised.