Finding the directory an application uses for temporary files
There are a few tools you can use to monitor file accesses but the two I'd recommend are (with their manual page descriptions):


opensnoop - snoop file opens as they occur. Uses DTrace.
lsof - list open files


Both are shipped with Mac OS and should do what you need. You'll need to run opensnoop in a terminal session before you start your cloud backup (it only displays changes after it's started) but lsof can display detail about all currently open files.