If 'ascending order' basically means 'arranged from smallest to largest in value', I suppose any difference in opinion here would depend on which letter, A or Z, is imagined to have the greatest value. I don't think it makes a lot of sense to say that either one does.
As Dave says, 'alphabetically' means 'from A to Z'. In English speaking cultures, this means that one looks from left to right or from top to bottom. The trouble with the word 'ascending' is that it literally means 'going up'. But it doesn't really mean going up vertically rather than going up in value. So a horizontal presentation of, say, the positive integers 1 to 9 in ascending order would mean that 1 is on the left: 1, 2, 3, 4, ... . But a vertical presentation of the same set in ascending order would then mean that the smallest value 1 is at the top and the numbers get bigger as you go down the list, which I think is counterintuitive given the literal sense of the word 'ascending'.
If you want to make it clear that you are arranging with Z at the top, then 'arranged Z to A' or 'arranged in reverse alphabetical order' is much better.