You must definitely make three inserts in the transaction. I would probably write a stored procedure to handle inserts.
EDIT:
. LAST_INSERT_ID(), . , .
DELIMITER //
CREATE PROCEDURE new_engineer_with_task(
first CHAR(35), last CHAR(35), email CHAR(255), tool_id INT)
BEGIN
START TRANSACTION;
INSERT INTO engineers (firstname, lastname, email)
VALUES(first, last, email);
INSERT INTO tasks (engineer_id, tool_id)
VALUES(LAST_INSERT_ID(), tool_id);
COMMIT;
END//
DELIMITER ;
:
CALL new_engineer_with_task('Jerry', 'Fernholz', 'me@somewhere.com', 1);