In the UK we have laws about transfer of personal data outside EEA. Then there’s the NSA to keep in mind, too.
Am I right in understanding that because DigitalOcean are a US based company, US law applies to all activities of non-US customers using resources in a non-US datacenter?
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Just to confirm, you will have to comply with US laws even if your droplet is in AMS.
You are correct.