That is because you wrote the wrong code:

print "Do they match ? : ";
print $filename_a =~ /\Q$filename_b\E/ ; # output is 1
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Always remember:

    /$regex/
    /\Q$string\E/
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If you use a variable as part of a regex, Perl needs to know if you want to interpret that variable as a string or as a regex. The default is to interpret it as a regex. If you want to use a string (from a variable) in a regex, then you need to tell Perl that by using \Q (or quotemeta, though this is can't be used as easily directly in the regex).

                - tye