I had never noticed the direction an arrow points in any sorted list before. But after looking at various operating system file list displays, online bank statements, email programs, and so forth, there is apparently an accepted standard that the direction of the arrow matches the current display state, not some future state. And in Manager, one does not click the arrow itself to change sort direction but rather the word heading of the column.
In every example I could find, the arrow points in the direction of the lesser, earlier, or alphabetically preceding entries. (All of these would be represented numerically by the smaller number.) This does indeed correspond to an upwards-pointing arrow when the sort is ascending and a downwards-pointing arrow when the sort is descending, just as @jon pointed out.
So far, I have found no references that define a standard. If you search the internet on the phrase “sort direction arrow standard” you will see that the question has been discussed on several other forums, but with no real resolution beyond noting what has been standardized within a given operating system or application. So perhaps Manager’s current convention is a legitimate as the opposite would be. Several of the online discussions point out that many common applications use other symbols entirely to signal sort direction.