How to mirror files on multiple servers on the Internet hot?

Question

File systems

There are 5 branches, ~70 users each. There is a general file storage ~ 2TB - office documents, tables, pictures. Branches are connected to the Internet at a speed of ~ 20 Mb / s. I want to make a file cleaning mirror in each branch. There was a modest question of synchronization of files. I did not master Rsync, it synchronizes only in one direction and my curvature led to the fact that sometimes old versions of files overwrote new ones. Syncthing is somehow stupid, it can "understand in the evening that in the morning" something has changed and start transmitting ...

In which direction can you read? I want something at the file system level, so that it determines that something is changing and the change itself is transferred to other mirrors, and not the entire files. How is it implemented in the clouds?

PS. Yes, debian servers. And no matter how there is no main server, each user connects to his own and files there as they please. And it all needs to be synchronized.
I don't think I'm the only one with this question, but somehow everything is deaf. Either everyone writes something of their own, or that ...