I'm not sure how this thing works. The description says it gives a free quality tier, so I assumed that it would be incapable of creating normal quality items, and would automatically upgrade uncommon to rare, etc... but it doesn't seem to have any higher chance to make quality items than any other machine with the same modules. Is this an error?

I didn't realize the innate 25% quality bonus it has because it doesn't appear in the alt+click menu or when you hover over it, only when placed. It also says that quality affects the quality % but my rare one has the same 25% bonus as the normal quality one. With 6 legendary quality 3's it would have only 62.5% which still wouldn't guarantee a quality upgrade. What am I missing?

You are missing that I forgot to change the description after I nerfed the quality assembler :-)
I'll change it. Thanks for the report.

Fixed.