So I'll take your challenge and say .. I think its working, if you dig into how its intended to work. Using your exact example dataset, I reformatted it for Date::Manip. Some may have other opinions on how to set the date, but this is compact and for me easy to follow:

use strict;
use warnings;

use Date::Manip;

my $dt1 = Date::Manip::Date->new();
my $dt2 = Date::Manip::Date->new();

$dt1->config("setdate","zone,Asia/Tokyo");
$dt2->config("setdate","zone,Asia/Calcutta");

$dt1->parse("20030502T07:53");
$dt2->parse("20030502T05:53");

if ( $dt1->cmp($dt2) ) {
   print "dt1 ftw!\n";
} else {
   print "dt2 ftw!\n";
}

print $dt1->printf("dt1 %c %Z\n");

$dt1->convert("Asia/Calcutta");

print $dt1->printf("dt1 %c %Z\n");
print $dt2->printf("dt2 %c %Z\n");
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Output is:

$ perl ./testdate
dt1 ftw!
dt1 Fri May  2 07:53:00 2003 JST
dt1 Fri May  2 04:23:00 2003 IST
dt2 Fri May  2 05:53:00 2003 IST
[download]