That assumes a private citizen can be charged with violating the civil rights of another.
Being a private citizen is no barrier at all. Here’s a link from the first page of the google search for “civil rights violation” + “double jeopardy”:
A guy is acquitted of murder, the Feds step right in with Violation of Civil Rights, he’s convicted, it’s not double jeopardy because you see it’s the Feds not a state, next case please.