A déjà vu is a repeat occurrence of an event which happens when the code of the Matrix is altered. Given that Matrix is an elaborate simulation program which cannot be stopped/rebooted every time some code is changed (as it contains biological systems like human beings who are not entirely under the machines’ control), when a sequence of events is needed to be changed in real-time, some initial portion of that sequence will be repeated because it takes some time to calculate the new sequence.
In order to understand this, imagine how the simulation might work. The simulation of the Matrix depends on the state 𝑠
at time 𝑡𝑖 and the choices 𝑐 of the humans and agents living in it at time 𝑡𝑖 and the rules of the Matrix 𝑟 at that time. Depending on these parameters, the state of the Matrix 𝑠𝑡=𝑡𝑖 proceeds to state 𝑠𝑡=𝑡𝑖+Δ
Let’s say that an agent decides to change the Matrix code at time 𝑡𝑖+Δ.
At this time he has access to 𝑐𝑡=𝑡𝑖+Δ, 𝑠𝑡=𝑡𝑖 and 𝑟𝑡=𝑡𝑖+Δ. The code change in the Matrix will change the rules of the Matrix, but the computation of these new rules will take some finite time 𝑡′. This cannot be kept precomputed because the state of the Matrix is not entirely predetermined. The choices 𝑐 of the humans in the Matrix are driven by a degree of free will.
After the elapse of 𝑡′, at time 𝑡=𝑡𝑖+Δ+𝑡′, the agent knows the new rules 𝑟′𝑡=𝑡𝑖+Δ which should have been used at time 𝑡𝑖+Δ instead of 𝑟𝑡=𝑡𝑖+Δ. Time can not be replayed, but Matrix being a simulation can be. So they replay the Matrix with the new rules 𝑟′𝑡=𝑡𝑖+Δ from the time 𝑡𝑖+Δ. Thus the events of the Matrix for time duration 𝑡′ are replayed with new rules 𝑟′, but with vastly different resultant states in the long run. Another way they could have done this is by resetting the memory states of all humans that are to be affected by these rule changes, but the earlier approach is much cleaner and less error prone.