I went to the psql commandline mode and entered the correct database and I can list all the tables.
Now, I tried the following commands:
copy some_table_name1 to '/var/lib/pgsql/csv_exports/some_table_name1.csv' csv header
copy some_table_name2 to '/var/lib/pgsql/csv_exports/some_table_name2.csv' csv header
And so on...
There was no error messages or anything after the commands and I used tab-button to ensure that I was always referring to correct table names.
After doing this to all the tables I went to the directory and there were no files at all.
Am I doing something wrong?
EDIT: I should clarify that I was looking to that directory, by using putty and WINSCP, on the server machine. The same where I ran the psql commands in.