Yes, that was true in the Corleone Family. Puzo made a point of Vito's carefulness in giving orders only to one person at a time--Hagen, his consigliere--to prevent having witnesses to his criminal orders in case someone turned rat. He also gave orders to Luca directly, without Hagen, but never to more than one person at a time.
Real-life Dons don't necessarily follow that pattern. The consigliere may be a respected Family elder, who's retired from active racketeering and is functioning as an adviser to the Don. Or the consigliere may be one of the caporegimes, who has people under him and rackets to look after in addition to his adviser role. Sometimes the roles are interchangeable: one of the Federal surveillance tapes caught John Gotti telling Sammy Da Bull: "What would you like to be--underboss, consigliere...whatevever makes you feel better."
Modern Dons are seldom as careful as Vito in passing on orders without witnesses. That's one of the main reasons so many of them have been ratted out, and have ratted out others in return.