Sorry, I'm having trouble understanding the details of the question.
If you are asking about how this form of clientside prediction works, it typically involves:
1) The client sends a steady stream of input packets to the server at a high rate.
2) The client predicts the result of those inputs while waiting for the server's response. The prediction is strictly for the sake of clientside responsiveness and have no impact on the 'true' state of the simulation. The true state is defined entirely by the server.
3) The server takes into account the stream of inputs while updating its simulation. The serverside simulation never directly adjusts object positions according to user input- instead, it simulates every frame of gameplay logic so there are no discontinuities. The server then sends out authoritative state updates based on the result of the simulation to all clients.
4) When a state update from the server arrives on the client, the client adjusts its view of the world to match. Since the message from the server represents a simulation state that appears to be in the past from the perspective of the client (due to the client's prediction), the client must resimulate from the server-provided authoritative state to a new predicted state again.
This isn't the only way to do things, of course. This particular approach avoids a wide class of cheats and maintains reasonably good clientside responsiveness, but costs a significant amount of computation on the client during corrections. For physically difficult simulations, it can become too expensive.
If you haven't already read them, I'd recommend scanning through all of the relevant gafferongames