Creating a MySQL Trigger
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;