I have default Date created, old -> new, and some specific albums with automatic order Date created, new -> old; that works. I presume that Date posted, new -> old as automatic order would work as well. Note that under Admin Albums Manage the manual order is always the upload order unless rearranged, but the normal gallery view is sorted according to the settings (or the sort order set in the album view).

there might be multiple causes here :
-be sure when viewing the album on the public side you don't have set a specific sorting
-when changing the sorting option on the admin page, the list of thumbnails you see for the manual ordering is not refreshed, but on the public side it is
-when creating a new album, you might need to set again your sorting option: i don't remember and couldn't find out on my gallery quickly the answer