What I see is the reference $ref_sub being assigned to @files

No, the result of calling the referenced code is assigned.

@files is a misnomer. "In list context, the iterator returns a list containing $dir, $file and $fullpath", the directory in which the next file is located, the name of the next file and the path to the next file.

am I supposed to put something in the parens after $ref_sub->(HERE) ?

No. The iterator has no parameters.

Is there a way that I can put my anonymous subroutines down in the bottom of my file

Given there's no reason for it to be anonymous in your case...

what are examples of something I would use there for \%options?

They're listed under "CONSTRUCTOR PARAMETERS".