How do savings run through payroll?

Exactly like the Set & Spend budgeting feature you will likely have enabled already.

Each payday's saving is a deduction, handled in the same deductions process as your other Aslan payroll deductions. It counts against the employee's allowance, locks at your payroll cut-off and settles on payday. It is taken from net pay, after tax, National Insurance and your other deductions.