Yes, player movement replication and prediction is implemented in UE4 as points out.
However it has changed locations from the days of UE3 (where it was in the PlayerController) to the CharacterMovementComponent for Characters in UE4. Prediction and correction when the character strays too far from the server’s authoritative position is implemented, as well as a Client authoritative mode that can be enabled. It’s fairly complex, but you can get a grasp of it by looking at the INetworkPredictionInterface implementation in UCharacterMovementComponent, as well as the related SavedMove processing in there that replays moves on the client when they receive a correction.
Vehicles using UWheeledVehicleMovementComponent also support replication to/from the server basically by replicating the input which drives the remote simulations. This is a simpler example but may server as a good starting point.