As you probably know, I'm using my new Blork tool to do all my link publishing these days. My links flow, through RSS, to other Blork users. And to Twitter, of course. And now they flow to a new place: Tumblr.
I know that Tumblr has them in the correct order in its database because when I go to the dashboard they are in the right order.
PS: My links flow to Tumblr through its API. I'm not using their RSS import feature.
Update: The problem was mine. My (new) code had a bug -- it was updating each of the last 20 items every time it checked. Once it settled down to only updating when the items changed -- and that's rare -- everything worked as you thought it should. So it was my problem, not Tumblr's.