For perhaps a better understanding… imagine that you have chest that can be opened by a client (with repNotify). When another player connect to the server (or player who was far away, not relevant) he will receive the update about chest (via repNotify) when he became relevant for that actor.
As for the priority of whether to put the functions first on the client and then on the server, according to my logic, since there is small delay on the server (commands are sent remotely), it is probably better to perform first on the server and then on the client. The client will not see any difference in repositivity. Although this won’t have much of an impact, because all will be probably executed in the same tick on the client side.