If I understand your question correctly, you are saying that you have seen cases where time is included in the calculation of the radial distribution function (RDF).
The RDF itself does not depend on time (and its calculation does not depend on any timestep). That is, the RDF is calculated as an ensemble average, so that either molecular dynamics or monte carlo could be used and it would make no difference.
On the other hand, if you have a system which is undergoing large structural changes over time, one could calculate an RDF over a sliding window of a trajectory to get a better view of what transformation is taking place. So, in this case, the RDF you are calculating for each window is not necessarily the equilibrium RDF, but is more like a semi-local (in time) RDF.
For instance, if one were heating up a system throughout the course of an MD simulation, then taking various slices of the total trajectory and calculating some RDFs would give you a picture of how the structure is changing with temperature. None of these RDFs, however, are necessarily the equilibrium RDFs you would get if you ran a full simulation at that particular temperature.