As it was pointed out by @Paulpro and @Alexey B. the most parts of it worked already, but I couldn't see it right away, maybe because I didn't reload my bash environment properly. But after that I faced other issue with npm outdated that was caused by the registry url. It turns out npm can only have one registry url, (which is pretty crazy) and if you want to use private and public npm-modules you have to proxy the public npm-module registry through your private registry. Luckily fury.io supports that, so in my case instead of using this:
//.npmrcregistry=https://npm.fury.io/AUTH_TOKEN/me/i have to use this:
//.npmrcregistry=https://npm-proxy.fury.io/AUTH_TOKEN/USER_NAME/UPDATE:It is possible to work around the problem (npm is tied to only one registry). First you have to add a scope to all of your private packages.Now with .npmrc you can link the registries for the scopes, and you no longer need any proxies at all.
//.npmrc@project_a:registry=https://npm.fury.io/AUTH_TOKEN/USER_NAME/@project_b:registry=https://npm.fury.io/AUTH_TOKEN/USER_NAME/@company_a:registry=https://npm.fury.io/AUTH_TOKEN/USER_NAME/