A reading is a record-producing event

Before the readout, the preparation contains quantum correlations between a clock and a system. After the readout, the accessible interface contains a finite classical label and a conditional system. The correlations supply the relational description; Enter supplies the chosen operation that makes a classical label available.

The operation does not create the family $U_S(t_k)$ from nothing. Its dynamical content was already fixed by the preparation, constraint, and clock calibration. Enter realizes extraction of that content.