On INSERT to a table INSERT data in connected tables

You might want to read about using Drupal hooks to add extra code to be run when a user is registered. Once you know how to use hooks, you can write code (in a module) to insert a corresponding record in the 2nd table. A good candidate hook to use here would be hook_user for Drupal 6 or hook_user_insert for Drupal 7.

The REFERENCES you read about is part of an SQL command to define a foreign key constraint from the second table to the first. This is not strictly necessary to solve your problem, but it can help in keeping your database consistent. I suggest you read up on database structures and constraints if you want to learn more on this topic.

pgAdmin is just the GUI. You mean PostgreSQL, the RDBMS.

A foreign key constraint, like you have only enforces that no value can be used, that isn't present in the referenced column. You can use ON UPDATE CASCADE or ON DELETE CASCADE to propagate changes from the referenced column, but you cannot create new rows with it like you describe. You got the wrong tool.

What you describe could be achieved with a trigger. Another, more complex way would be a RULE. Go with a trigger here.

In PostgreSQL you need a trigger function, mostly using plpgsql, and a trigger on a table that makes use of it.

Something like:

CREATE OR REPLACE FUNCTION trg_insert_row_in_tbl2()
  RETURNS trigger AS
$func$
BEGIN
   INSERT INTO tbl2 (my_id, col1)
   VALUES (NEW.my_id, NEW.col1)     -- more columns?

   RETURN NEW;  -- doesn't matter much for AFTER trigger
END
$func$  LANGUAGE plpgsql;

And a trigger AFTER INSERT on tbl1:

CREATE TRIGGER insaft
AFTER INSERT ON tbl1
FOR EACH ROW EXECUTE PROCEDURE trg_insert_row_in_tbl2();