There are a number of factors that impact whether a taxpayer (or business) needs to file in a particular state regardless of whether they are domiciled or "incorporated" in a particular state. This has to do with what is known as nexus (contact) creating activities.
Additionally, states have different types of tax which in general are a state income tax or a franchise tax which is essentially a privilege tax to do business in that state.
I have attached a link to get you started in this area, but it may be in your best interest to discuss this with a tax professional.
https://www.ftb.ca.gov/file/business/types/corporations/s-corporations.html
*A reminder that posts in a forum such as this do not constitute tax advice.
Also keep in mind the date of replies, as tax law changes.
