Just from looking at the documentation to File::Find::Rule, I'd say something like this:

my $rule =  File::Find::Rule->new;
$rule->file;
$rule->name( '*.tmp' );  #find all xml files
$rule->mtime("<$timeback");

my $file = "output.log";
open(OUT, ">$file");

$rule->start($startdir);
while (my $file = $rule->match())
{
  print OUT $file, "\n";
  ## move and tar it here
}

close(OUT);
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(Completely untested of course - I don't even have F::F::R installed...)