State Payroll Rules

I am trying to understand how one determines which state payroll rules apply to individual employees, for example:

Employee A resides and works in State X. State X rules apply.

Employee B resides in State Y but works in State X. State X rules apply.

Employee C resides in State Y and works from home for company located in State X. Which state rules apply?

Employee D resides in State X and works remote from State X for 3-4 months at a time. Which state rules apply?

Employee E resides and works Internationally for Company in State X. Which state rules apply?

Could the decision be based on where the employer pays State Payroll Taxes? Or where the employee pays State Income Tax?

I am working on a prepaid project that has state payroll compliance requirements and I don't want to spend my time going with the wrong assumptions.