This is a typical MySQL thing and can usually be circumvented by selecting from the table derived, i.e. instead of
FROM manager AS m2
use
FROM (select * from manager) AS m2
The complete statement:
UPDATE manager
SET status="Y"
WHERE branch_id IN
(
select branch_id
FROM (select * from manager) AS m2
WHERE (branch_id, year) IN
(
SELECT branch_id, year
FROM branch_master
WHERE type="finance"
)
);