I should have qualified what I said. There are three different types of lists for looking at Unsourced profiles.
1. The links to Unsourced lists that are divided by century, as shown in the Team Space Page, are listed in Birth Date order as I said. As you edit and save them, the list remains static -- it doesn't change until the next week's system update.
2. If you go to the Unsourced Profiles Category pages and work directly from the profiles on those lists, they are all sorted by LNAB. After you save a profile, that profile no longer shows up on the list (assuming you removed the Unsourced category). You need to refresh the page to see the profiles disappear.
3. You can also generate a list on WikiTree+. Those can be sorted in several ways: by name, creation date, birth date, death date, birth location, or death location. Those lists are also static - they do not change - after making edits to the profiles.
There are pros and cons to using the different types of lists. It's a matter of personal preference, but it's probably easiest if everyone uses the same type of list.