From the doc to Date::Manip:

VERSION 5 AND VERSION 6

Date::Manip version 6.00 was a complete rewrite of the module (for more information, please refer to the Date::Manip::Changes5to6 document).

The document linked to in that Readme contains all you need to know about the changes to TimeZone handling in Date::Manip, including at http://search.cpan.org/~sbeck/Date-Manip-6.58/lib/Date/Manip/Changes5to6.pod#TIME_ZONE_SUPPORT.

Personally I use DateTime for all date ... er, manipulation. (Note that you should let it handle Daylight Savings Time automatically for you, i.e. don't specify CST but rather "America/Chicago" or similar.)

$ perl -MDateTime -E '
my $dt = DateTime->now;
say join " ", $dt, $dt->time_zone_short_name;
$dt->set_time_zone("America/Chicago");
say join " ", $dt, $dt->time_zone_short_name;
'
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Output:

2017-05-01T16:53:29 UTC
2017-05-01T11:53:29 CDT
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Hope this helps!

Update: added DT example