The log confirms that Hazel is matching the rule on the file.
I'm downloading a daily crossword from New York Times that has an extension of .puz. I want Hazel to monitor Downloads folder and move this file to a different directory (on my iSync drive, by the way).
Hazel is copying the file over and instead of throwing away if duplicate, it renames it - so that's causing the multiple files. It does this over and over. And never "moves" the file from Downloads - it stays there.