Not true.
When Caesar had to hide from the proscriptions of Sulla as a young man, his family was not molested. His mother Aurelia and her brothers the Aurelii Cottae, although the Aurelii had been supporters of Marius, were untouched.
When the Second Triumvirate (specifically Mark Antony) put Cicero to death, his son Marcus was passed over and spared, while Cicero's brother Quintus, who'd been a legate of Caesar's, and Quintus's son Quintus, were both executed. But the slave who betrayed them both was complaisantly identified by Sulla's men to Quintus's wife Pomponia (the sister of Atticus, Marcus Cicero's great friend and brother-in-law), who presided over the slave's grisly death: she forced him to cut chunks off himself, cook them up at table, and eat them, in a scene that probably inspired the Ray Liotta payoff scene in Hannibal.
It wasn't all one way or another; the Romans didn't know what totalitarianism was, until Diocletian imported its principia from Egyptian temple practice in about 305.