If it's appropriate, you can change the state tax setup on the employee record and then future paychecks will use that setup. Doing this won't technically mess up the existing paychecks or tax reporting. QuickBooks can handle an employee who is subject to taxes from different states over time, such as when an employee moves from one state to another. In most cases it can also handle the case where an employee lives in one state and works in another. (However, it can't double-tax an employee for the same type of tax, like state withholding, for more than one state on the same paycheck.)
However, in your case be sure to only make changes if they're required, and to make the changes correctly. It's not always intuitive.
For example, an employee has to work in an alternate state for more than a set amount of time, different per state, in order to be subject to that state's payroll taxes. The rules vary per state.
At the same time, because you as a company are operating in another state, you'll very likely have created a "nexus" there, which means the company is subject to that state's employment rules, which you are expected to know as an employer.
