You understand the intent of the marker tags, let's just make sure you have added them correctly to your books.
The default of '~,Catalog' is two tags - '~' and 'Catalog'. There should not be a space in between those tags in the EPUB/MOBI Catalog dialog.
You've changed that to '~,Completed'. That tells the Catalog builder to skip any books that have the tag '~' or 'Completed' when building the catalog.
On the books which you've completed reading, if you inspect their metadata, in the tags field you should have 'Completed', plus any other relevant genre tags - Fiction, ... They should be in a list with commas separating the tags, and no spaces:
Code:
Completed,Fiction,Adventure
Is that what you've done? If so, post a log so I can take a closer look.
One other tip: when you're experimenting with tags, drag-select a couple of books with the tags of interest, build it as an epub, and look at the results with calibre's built-in viewer. That gives you a very quick means of confirming that your tag set is working the way you expect it to. By selecting two or more books in the main window, only those books will be candidates for the catalog. And remember to use the bulk metadata tag editor to set/clear a tag for a group of books. Less likelihood of typos.
G