Although the Getopt::Std documentation doesn't seem to mention it, -t and -s are special. Consider:

use strict;
use warnings;
use Getopt::Std;
use Data::Dump::Streamer;


testSwitches (qw(-p -q));
testSwitches (qw(-s));
testSwitches (qw(-t));
testSwitches (qw(-s -t));
testSwitches (qw(-p));


sub testSwitches {
    local @ARGV = @_;
    my %opt;
    my $test;

    print join (' ', @ARGV), "\n";
    getopt ('st', \%opt);
    Dump \%opt;
    print "\n";
}
[download]

Prints:

-p -q
$HASH1 = {
           p => 1,
           q => 1
         };

-s
$HASH1 = { s => undef };

-t
$HASH1 = { t => undef };

-s -t
$HASH1 = { s => '-t' };

-p
$HASH1 = { p => 1 };
[download]

Is this some sort of *nix convention perhaps?

Note that you could use exists for your test instead of defined. You could also reduce the number of parenthesis to make the code more readable:

if (! exists $opt{s} and ! exists $opt{t}) {
[download]

Update: Struck silliness. Left code as a nice template for playing with/testing/demonstrating option processing.