The problem is that your final print statement is being sent to the end of output.txt instead of the console. STDOUT is still redirected at that point. There are several ways to remedy the situation; here is one using backticks (`) to capture the output of the script you run:

use Fcntl;
use Tie::File;

open my $out, ">", "output.txt" or die "$0: open: $!";
my $run = "./SCRIPT.pl";
print $out "##Start of SCRIPT.PL##\n", `$run`;
close $out;

tie my @rows, 'Tie::File', 'output.txt', autochomp => 0 or die "error:
+ $!\n";
print ":$rows[-1]";
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In the above case there is no pressing need to use Tie::File which will be less efficient. Hopefully this was just a small snippet of a larger work where its use is more warranted. :o)