SQL> create table person
  2  (employee_id varchar2(10) primary key,
  3   position_id varchar2(10),
  4   some_other  number
  5  );

Table created.

SQL> create table position
  2  (position_id varchar2(10) primary key,
  3   current_inc varchar2(10),
  4   another     number
  5  );

Table created.

SQL> insert all
  2    into person (employee_id, position_id, some_other) values ('1', null, 100)
  3    into person (employee_id, position_id, some_other) values ('2', '20', 200)
  4    into position (position_id, current_inc, another)  values ('10', null, 1000)
  5    into position (position_id, current_inc, another)  values ('20', null, 2000)
  6  select * from dual;

4 rows created.

SQL> select * from person;

EMPLOYEE_I POSITION_I SOME_OTHER
---------- ---------- ----------
1                            100
2          20                200

SQL> select * from position;

POSITION_I CURRENT_IN    ANOTHER
---------- ---------- ----------
10                          1000
20                          2000

SQL>

SQL> create or replace trigger trg_pers
  2    after update of position_id on person
  3    for each row
  4  begin
  5    update position p set
  6      p.current_inc = to_char(sysdate, 'hh24:mi:ss')
  7      where p.position_id = :new.position_id;
  8  end;
  9  /

Trigger created.

SQL>

SQL> update person set
  2    position_id = 10
  3    where employee_id = 1;

1 row updated.

SQL> select * from person;

EMPLOYEE_I POSITION_I SOME_OTHER
---------- ---------- ----------
1          10                100
2          20                200

SQL> select * from position;

POSITION_I CURRENT_IN    ANOTHER
---------- ---------- ----------
10         08:06:28         1000
20                          2000

SQL>