Michael said that he worked in a bank for three years.
This sentence is fine and accurately reports what Michael said, but it does introduce some ambiguity. Was Michael saying that he has worked in a bank for the past three years (and still works there) or that he worked in a bank for three years in the past (and is no longer working there)?
Michael said that he has worked in a bank for three years.
With no doubt or ambiguity, this statement would correspond to: "I have worked in a bank for three years," said Michael.
Therefore, in order to clearly communicate Michael's intent when he says, "I worked in a bank for three years" (simple past), we need the past perfect:
Michael said that he had worked in a bank for three years.