stop the server, then download the world
Ugh. Sorry. My mistake.
I had downloaded the world with the server stopped. But I made a single character typo in the name of the world in the server.properties file. When I started my local server it "auto created a new world" instead of telling me that the configured world did not exist. ( Sigh. ) And the spawn point resembled the world I was expecting.... ( So I jumped to the conclusion that I downloaded the original world instead of the current state.)
I did get a "current copy" of the world when I did a manual backup with the Aternos server while it was stopped. Thanks.