Postgresql update timestamp without timezone to have timezone
I also don't see the problem

Create sample data,

CREATE TABLE foo(ts) AS VALUES (
  now()::timestamp without time zone
);


Display it,

TABLE foo;
             ts             
----------------------------
 2017-09-30 14:25:24.954084
(1 row)


You can see in the above no tz in output. Now let's change to use a with time zone.

ALTER TABLE foo
  ALTER COLUMN ts
  SET DATA TYPE timestamp with time zone;


Here is the output, notice you have a tz of -05

TABLE foo;

              ts               
-------------------------------
 2017-09-30 14:25:24.954084-05
(1 row)


What's your result of SHOW TIME ZONE?

Interestingly though, I do see what you're talking about with,

# SELECT now()::timestamp with time zone::timestamp;
            now             
----------------------------
 2017-09-30 14:27:53.061616
(1 row)


However, we have to know what you're asking.