Here is an example that should help. If you have a timestamp with a timezone, you can convert that timestamp into any other timezone. If you haven't got a base timezone it won't be converted correctly.
SELECT now(),
now()::timestamp,
now() AT TIME ZONE 'CST',
now()::timestamp AT TIME ZONE 'CST'
Output:
-[ RECORD 1 ]---------------------------
now | 2018-09-15 17:01:36.399357+03
now | 2018-09-15 17:01:36.399357
timezone | 2018-09-15 08:01:36.399357
timezone | 2018-09-16 02:01:36.399357+03