It seems like implementing minimum wage changes could fall on many departments - wage and compensation, HR, payroll.... where in your company do the responsibilities of implementation fall? Is the payroll department responsible?
well, it would be me.... but I wear both hats (HR and payroll) for a group of small companies.
To me, there should be interaction and working together between HR and payroll. Unless there is a parameter where the minimum rate is changed for the whole payroll system and all employees (rather than individually entered info), I would want someone other than payroll signing off on any wage changes. Even though I wear both hats, I ask that managers and execs give me any pay increases in writing.
When the whole increase to exempt pay came last year, from an HR standpoint I was responsible to look at all exempt salaried employees, see who feel in the affected range and then help the executives decide individually what to do. Then I went into payroll and implemented (and undid at the last minute) their choices.