Not consistent. Plenty of profiles have the source as, roughly, "personal recollection" or "as related by living relative" and are not tagged as lacking sources. Not that worried about whether the sources notice is "correct", more that it might get deleted or somesuch.
It will be 34 years before those dates are on the NSW index.I've tried Trove, ryersonindex.org, and Google newspapers, but no sign of birth notices or any newspaper attention of any kind.
I'm told elsewhere it won't get deleted or anything like that, and to just let it be. I think I've done all I can think of at the moment to find other sources.
Think there is no automatic removal of unsourced tag.