Gregory's Server
@mariusor there's the prevalent kind of user: they want everything to "just work". Making them click buttons to re-fetch their friends' friend lists makes it too cumbersome and gives the impression of a buggy product.
VK used to have this problem where different databases on different servers would get out of sync and there would be notification counters when you don't actually have any. There was a button in settings to "recount" them. It was eventually fixed and the button was removed.
@grishka it sounds like you are thinking of a different use case than I understood from @liaizon 's top post. I thought the idea was that when you go to a remote user's profile on your own instance, you can see their followers. So the intention of the initial user is already there: click followers link in a remote user's profile.
In this case the remote instance should just be another data store for the one the initial user is browsing at the moment.