I struggle with this as well and having the team look into this. Not too many of us use Parallels but I will see what I can find. This is not an issue exclusively related to EndNote as many other types of files have the cross-platform confusion issue - even when EndNote is not installed on either partition of a Macintosh using Parallels.
I have tried the File Association settings in Windows: Control Panel >
All Control Panel Items > Default Programs > Set Associations - where Windows does allow us to set file associations with Macintosh programs but this is not working for me. Meaning I can set it on Windows but the changes then do not seem to be recognized on the Macintosh side.
This issue is a bit pronounced with EndNote since EndNote manages several different types of auxillarly files - Styles, Imports, Libraries, etc.
One workaround might be to use Firefox as your web browser on the Macinsoth as Firefox should allow you to control file export extensions from web-based databases. Safari does not seem to be as flexible in my quick tests.