There is a difference between State Payroll Tax and the PAYG (pay as you go) Withholding. Saasu automatically handles PAYG withholding calculations but does not calculate State Payroll Tax.
As such it is important for you to check the value of your payroll against each states payroll tax thresholds. Each state/territory has an Office of State Revenue (OSR) or equivalent and these authorities will be able to provide you with details of thresholds and amounts to pay to them as a state authority. They will quite often have tools on their respective websites to facilitate this calculation.
You will have to look at the value of your payroll for a period (month, quarter, year) and then apply relevant percentage calculations to get to the value of your liability to the relevant authority.
Once you have calculated how the value of state payroll tax you are required to pay simply enter in a purchase against the relevant revenue office as a contact to an expense account as instructed by your advisor. Then once you are ready to pay this simply apply a payment against the purchase you just created in Saasu.