An Operator will receive a "copy" of your logbook—a PDF version of your daily work record—only if they are designated as a TSL Holder for that particular work day and after you lock the shift.
However, as long as your relationship with an Operator is active, they will have complete access to your entire logbook history and your current work-time balances in real-time. Should your relationship with an Operator become archived in the future, they will only retain access only to the "copies" of the logbook for the days you worked under their TSL.