I have looked at the last order we have in the office re a change from IPP to 37/41 via the CoA.
The CoA explicitly stated in that particular case that the orders “begin to run from today” i.e., the date the CoA considered the case and made the orders.
It quotes s29(4) Criminal Appeal Act 1968 as enabling it to make orders in those terms “(4)The term of any sentence passed by the Court of Appeal under section 3, 4, 5, 11 or 13(4) of this Act shall, unless the Court otherwise direct, begin to run from the time when it would have begun to run if passed in the proceedings from which the appeal lies.”
So, whilst it is possible for the new order to be in effect backdated, the CoA simply does not need to do this and can simply quash the prior order on the day and make a new one which operates wef that same date.
I do not know what the CoA order in CS actually said so it could be either. Only looking at the CoA order will one be able to tell.