How is the Employer's contribution to taxes on tips managed in the payroll process?

Is the Employer expected to contribute to these taxes with each pay cycle, or is it handled on a quarterly basis?

It is handled on each pay cycle. For tips that are already paid, both the Employee and Employer portion are taken out at the time payroll is ran. When running payroll, the final page before submitting payroll will give you a breakdown of these taxes (both from the Employee and Employer). Simply click on the Taxes tab, or select View Payroll after you have submitted payroll: