For proxy access, institutions need to set up a proxy server (EZproxy is a common example) on their side, and the proxy IP is added to their institutional account at Springer. Their individual users can log into the proxy (looks like, for example, a username/password box on a library login page), and then are recognized by Springer Nature Link as if they come from the IP range of the institution. For proxies, individual usernames are handled entirely on the institution's side.
See configure a proxy to work with Springer Nature Link for additional information.