Simulator in Private Outsourced Computation over Outsourced Datasets
The objective of the simulator is to make the simulated world (often called the ideal world) indistinguishable from the real world (running the actual protocol). See my write-up on the UC framework here for more detail.

In the proof setup, the entity attempting to distinguish between the two worlds is often assumed to provide the inputs to the parties. That keeps things as generic as possible.

So, what should be done is have $\mathcal{Z}$ pick the inputs for the parties.