Does your restaurant staff management software work out wages from the hours?

No, and that is a choice. Reports → Hours worked shows hours only: every stretch with the clock in, the clock out, the break taken off and the worked total, and a total per person. There are no rates of pay and no money anywhere on the screen, so you can show it to a manager without showing anybody what anybody earns. Download CSV gives you one row per stretch and a totals block per person, which is the sheet you hand to whoever does payroll. Multiply by the rate in your own spreadsheet. The Staff, PINs and hours tab in the docs explains the report column by column.