According to the E-Commerce Directive 2000/31/EC, the place of establishment for a company providing services via an Internet website is the place where the service provider effectively pursues an economic activity through a fixed establishment for an indefinite period of time. The presence and use of the technical means and technologies required to provide the service do not, in themselves, constitute an establishment of the provider. The place of establishment is determined by the place where the decisions about processing are made, not by the place where the technology supporting the website is located, where the website is accessed, or where the customer's Internet service provider is located. This is confirmed by the GDPR, which applies to the processing of personal data in the context of the activities of an establishment of a controller or a processor in the EU, regardless of whether the processing takes place in the EU or not. Reference:
E-Commerce Directive 2000/31/EC, Article 2(a), Recital 191
GDPR, Article 3(1)2