Do accountans/auditors have to do their work manually to master their job or are Accounting/auditing applications good enough to get the job done?

The auditor must be proficient and competent in order to carry out an audit. The auditor must be based on his experience and control skills; For me I am for manual control

Not necessary, some companies follow the manual system and there are also some accountants and auditors who works manually or both ways

Not necessarily and in case of large organisations it will not be practically possible.  Accounting application also give the same perspective as the accounting entries are made based on physical documents.  So, it is a combination  of both manual and automated method.