That error is specific to DFSR. So multiple users accessing a file on Site1 server wouldn’t generate that issue. The error is there because something modified the file on Site2 server and something else modified it on the site1 server.
These modifications don’t have to be users accessing the data and changing things. It could be something as simple as the archive bit being cleared by the backups running on the site2 server.
Here’s a blog post on troubleshooting a change storm but it should give you details to dig into the logs to see what is being changed. https://blogs.technet.microsoft.com/askds/2012/06/01/whats-causing-that-dfsr-change-storm/
What ever processes you have running on the Site2 server, make sure they are not modifying any of the data or metadata of the DFSR files.