Where a downloading file goes should be a setting in your browser preferences.
Thanks for reaching out and trying to help. Your advice was really invaluable, however despite all changes in the settings, I am still having the issue.
It looks like the issues begin when you save an image to the Library as liked. I just tried with ‘DRONE’. I didn't have a file in my Library associated with Drones and the first image was saved in my local drive. However, the moment I created a file in my Library with ‘Drone name’ all images were instantly opened in Adobe Illustrator. Very frustrating as it takes ages to open the file in the Adobe Illustrator, instead of checking it instantly in Photos. Adobe Support was absolutely useless.
Well, I'm on Mac, but there must be a Windows equivalent (mustn't there?) where the contextual menu for each file gives access to an info window where you can indicate what app should open a particular file, with the option to have that application open all files of that kind.
Sorry for the delayed response. Looks like you are downloading the preview of stock files from CC libraries. Could you please confirm what type of file is this JPEG/ PNG, etc.?
You just need to change the default app to open these files from Illustrator to your desired application.