This mis-states the facts at issue. Article I states it very well:
"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.
A sitting President is immune from prosecution, but once removed by impeachment or the passage of time, "[He] shall nevertheless be liable and subject to Indictment, Trial, Judgment and Punishment, according to Law"
“according to law” being the operative words in your post.
Given the wildly extreme hypotheticals discussed this morning, one would think that impeachment and conviction would be practically automatic if credible evidence of murder or selling nuclear weapons to enemies was produced.
I don't believe the "passage of time" departure from the Presidency opens up the President to be charged for anything he did in office that the opposition didn't like. I believe the "impeach, convict, indict, and prosecute" model implies the opposite too, that is, absent impeachment and conviction, a former President cannot be indicted and prosecuted for acts undertaken while President.
-PJ