What happens is that there are two processes running from the exec line and the kill will only kill of the parent of the two processes.

I don't know why a redirection would create 2 processes, but if I wanted to get the output of the child, I would just spawn a child with a filehandle attached, and read it from the parent. I would change the spawn function as follows. WARNING: I haven't tested this at all):

sub spawn
{
    my ($timeout, @cmd) = @_;

    defined( my $child_pid = open(CHILD_OUTPUT, "-|" )
        or die "fork: $!";

    if ($child_pid)
    {
        # parent
        eval
        {
            local $SIG{ALRM} = sub { timeout($child_pid); };
            alarm $timeout;
            while (<CHILD_OUTPUT>)
            {
                # log it
            }
            close(CHILD_OUTPUT) or warn "process $child_pid exited: $?
+";
            alarm 0;
        };

        if ($@)
        {
            print "oops: $@";
        }
    }
    else
    {
        # child
        exec @cmd or die "exec: $!";
    }
}
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