Typically what you do when rotating log files is to rename the current log file - and leave it alone for a while. Many daemons open the log file once, and only close it when they are done. Renaming an open file is ok, the process is only using the handle, it doesn't care about the rename.

It may be that the main rsynd process needs to be send a SIGHUP - but you'll have to check that. Sometimes a daemon opens a log file, and then when it has to do work, it forks, giving its child an open file handle. Typically, on a SIGHUP the main daemon closes and reopens any handles. But if the main daemon doesn't keep open handles, there's no need.