PostgreSQL custom domain with trigger

Since your two types are composed from the same basic types in the same order, they are compatible with each other. So the return type will be the same for functions using them - if I understand correctly, your problem is you want to have the different names of the returned columns depending on the type.

This cannot be done from the database, but you can easily do it from your application. It can be done like (ugly pseudocode)

if type == 1 {
    execute("SELECT 1 AS id_normal_number, '00001' AS normal_number FROM your_function()")
} else {
    execute("SELECT 1 AS id_special_number, 'S0001' AS special_number FROM your_function()")
}

ie. changing only the names, but using the same DB function. Or you can invoke two different functions, this way you can avoid dynamic SQL, which may be desirable for readability/performance, depending on some circumstances.

Try

CREATE TRIGGER tg_ai_tablea
AFTER INSERT ON tablea
FOR EACH ROW
  INSERT INTO tableb (userid, value)
  VALUES (NEW.userid, CASE NEW.type WHEN 'admin' THEN 1 WHEN 'user' THEN 2 END);

Here is SQLFiddle demo

You can also consider instead of storing value just evaluating it on the fly

SELECT b.userid, 
       CASE a.type WHEN 'admin' THEN 1 WHEN 'user' THEN 2 END value
       -- , other columns from tableb
  FROM tableb b JOIN tablea a
    ON b.userid = a.user.id;