I am writing a theory chapter on the RANS equations for my thesis and I am slightly confused about Reynolds and time averaging. Maybe it's a bit late to be confused but better now than never.

In CFD I'm aware that RANS codes are used for steady-state cases and are not suitable if one wants to capture time dependant phenomena. The thing that is confusing me, however, is that I thought Reynolds averaging was a technique where the variable is decomposed into a mean and a fluctuation term. My confusion is that I thought the mean could be taken over time, space, phase, ensemble ecc... So how are RANS codes automatically time averaged?