You are responsible for paying taxes in any jurisdiction in which you have sufficient nexus to justify taxation. For individuals, residence is the generally accepted means for establishing residence, but some states also use employment as a nexus (such as New Jersey). For businesses, nexus is much broader, and generally includes any state in which the business is incorporated or registered to do business, any state in which it has facilities or employees, and (for sales and GST taxes) generally any state in which a customer is located.

The Chicago tax would be most similar to a sales/GST tax. Under well-established state and local tax principles Netflix, et al, could generally be required to collect the Chicago tax on sales/services to Chicago customers.