It is not enough to unlock the same account in the primary database. This is because the standby is open read-only and cannot update any tables. When a user's account has to be locked on the standby database, it is locked only in memory there.
A privileged user (sysdba, the database administrator) must logon to the standby and unlock the account there. A message ORA-28015 "Account unlocked, but the database is open for read-only access" confirms that the account is now unlocked in the standby database. From then on, the user can logon to the standby database without getting any error.
ORA-28000 "the account is locked" in the standby database, even after the account was unlocked in the primary. (Doc ID 1600401.1)