Did you set your nameserver for the domain to digital ocean ones (in fasthosts it's under your domain > Manage Namservers) or did you just create NS records in your fasthosts DNS?
To move DNS to DO for your whole domain you'd need to use their nameservers unless you just want to delegate to them for a subdomain (e.g. example.com could technically have DNS hosted on fasthosts and have subdomain.example.com DNS hosted on DO, but I'm not sure that's what you're trying to do).