If I may add a few critiques...

  # Make sure no one else is using rsync
  pro_on=$(ps aux | grep -c rsync)

A better way to do that is with the flock utility.

  (
    flock -n 9 || exit 1 # Critical section-allow only one process.

    ...single thread shell script

  ) 9> ~/.empty_lock_file

Note that the flock utility is specific to Linux, but POSIX mkdir() is atomic and could be more portable.

  "${SOURCES[@]}"

POSIX shells do not support arrays. Iterating with read over a here document is more portable.

  minutes=$(($minutes - 1))

POSIX is specific that the $ prefix on a variable name can be omitted in an arithmetic expression.

  ECHO="/bin/echo"

Many shell scripts never use echo, and this is a good idea. 'NEVER use echo like this. According to POSIX, echo has unspecified behavior if any of its arguments contain "\" or if its first argument is "-n".' http://www.etalabs.net/sh_tricks.html

Perhaps use this instead, in a subshell to avoid stomping on variables:

  myecho () ( z=''; for x; do printf "$z%s" "$x"; z=' '; done; )