The program that open up on clicking the " edit original " depends on the file format of that particular file which you want to get opened.If the file is of an image format like .jpeg .jpg .png etc , usually MS Paint open up as it is the default photo editor in windows for the above file extensions.If the linked file is of .psd format,then the Photoshop will open up as it is it's default program.

So if you want to open Photoshop on clicking "edit original" for image files,simply go and change the default program for image files to Photoshop.

Open an image in your explorer > right click > Open with > Choose default program > Select photoshop !

Now you can open photoshop to edit the orginal files ( image files ) in illustrator.