The rule against prosecuting a sitting President is not a law, it is a Justice Department opinion and policy. The justification for it is that dealing with a criminal case would be severely distracting to the President, and thus harmful to the nation. Besides, the opinion goes on, any serious issue can be dealt with by impeachment. That reasoning obviously does not apply to a former President.
Article I, section 3, paragraph 7 of the US constitution says:
Judgment in Cases of Impeachment shall not extend further than to removal from Office, and disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States: but the Party convicted shall nevertheless be liable and subject to Indictment, Trial, Judgment and Punishment, according to Law. (emphasis added)
This clearly contemplates the criminal prosecution of a former office holder, after such a person was removed by an impeachment. There is no exception for a President. Therefor a President can be criminally charged and prosecuted for actions during the presidency, provided that the evidence to establish probable cause is there, and that a Grand Jury indicts said former President.
So far as I know there has never been a case where such a thing was done. President Ford's pardon of President Nixon stopped any Federal prosecution of him. I think there have been cases were former US Judges, after impeachment, were criminally prosecuted. But that is not quite the same thing -- no one claims that sitting judges are immune to criminal charges.
To be clear this would not apply just to issues that a President had been impeached for. A former President is no different from anyone else in this respect. Any such person can be prosecuted if there is probable cause, and convicted if there is proof beyond a reasonable doubt of criminal violation of some law, even if the violation occurred while the president was in office.