Two objects, two clocks
A birth, marriage or death entry is a living thing. It sits in a register, it can be corrected, and later events can be written beside it. A certified copy is not that entry; it is a picture of it, taken on one day by one officer. Everything you post abroad is a picture, and pictures do not update themselves.
Why the gap matters more on the Cuban route
Cuba has not joined the Hague Apostille Convention, so a British file for Cuba runs through consular channels and takes in more than one desk. Document legalisation for Cuba is therefore a longer errand than a single-stage route, and length is exactly what lets a snapshot drift away from the register it came from.
There is no such finished article as an apostille issued in Birmingham for use in Cuba, so do not plan around one. Plan around a chain with a consular ending, and treat the date on your certified copy as the start of a clock you would rather keep short.
What the British mark actually describes
The Legalisation Office compares the signature or seal on your sheet with its own record of British public officers and prints a certificate saying it is genuine. That statement is about a signature on a piece of paper. It is not a statement about the register, about the person named, or about anything that has happened since the copy was printed.
This is why an attached certificate cannot rescue an out-of-step copy. It confirms exactly what it says it confirms. If the entry behind your copy has moved, the mark on top is still honest and still useless for the point in question, because it was never looking in that direction.
Keeping the two in step
The practical fix is ordering, not paperwork. Get the certified copy from Holliday Street when the rest of the file is close to ready, rather than months ahead while other pieces are still missing. A copy that waits in a drawer ages against its own register, and nothing later in the chain repairs that.
If several copies are needed, order them as one batch on the same day so they all describe the same moment. Then move them through the stages together. A set that stays together tells one consistent story at the far end, which is worth far more than any single stamp on any single sheet.