I think that using Tie::File in this particular case (when sequentially iterating over the records) doesn't provide any advantage over simply reading line by line from a normal file handle (rather, it's likely to be slower, due to the much more complex things going on under the hood...).

That is,

tie my @file1_arr, 'Tie::File', $file1, mode => O_RDONLY;

foreach my $record ( @file1_arr) {
    # ...
}
untie @file1_arr; # finished with file 1
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would become

open my $fh, "<", $file1 or die "Couldn't open '$file1': $!";

while (my $record = <$fh>) {
    # ...
}
close $fh;
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(ditto for $file2)