Usually the copying program is doing it in blocks, not entire file at once. I don't think you can do anything to avoid this, you will have to adopt your algorithms to deal with this.
You can perform an attempt to open file with exclusive read rights, which should be granted to your program only when other program finished copying and closed file. Otherwise you will get IOException and you can wait for next change. But this doesn't mean you shouldn't deal with multiply change events. Opening text file in Notepad and saving it once in a while will generate change events, but file will not be locked all the time.
Another approach would be to collect touched files for a period of time, and when FileSystemWatcher stops generating events, process all files at once.