Don't forget to check the zip isn't empty, folks - otherwise the zip won't be created at all, and the server will issue no warning!
I used a certain loop to add files to the zip, and struggled with permissions and documentation for hours before I realize the loop ended up adding no file, even though addFile WAS called, but on a non-existent file.
This might be the reason your zips aren't popping up.
ZipArchive::addFromString