どハマりした。

exec のオプションを確認

docker exec --help

Usage:  docker exec [OPTIONS] CONTAINER COMMAND [ARG...]

Run a command in a running container

Options:
  -d, --detach               Detached mode: run command in the background
      --detach-keys string   Override the key sequence for detaching a container
  -e, --env list             Set environment variables
      --env-file list        Read in a file of environment variables
  -i, --interactive          Keep STDIN open even if not attached
      --privileged           Give extended privileges to the command
  -t, --tty                  Allocate a pseudo-TTY
  -u, --user string          Username or UID (format: <name|uid>[:<group|gid>])
  -w, --workdir string       Working directory inside the container

docker-compose exec --help

Execute a command in a running container

Usage: exec [options] [-e KEY=VAL...] [--] SERVICE COMMAND [ARGS...]

Options:
    -d, --detach      Detached mode: Run command in the background.
    --privileged      Give extended privileges to the process.
    -u, --user USER   Run the command as this user.
    -T                Disable pseudo-tty allocation. By default `docker-compose exec`
                      allocates a TTY.
    --index=index     index of the container if there are multiple
                      instances of a service [default: 1]
    -e, --env KEY=VAL Set environment variables (can be used multiple times,
                      not supported in API < 1.25)
    -w, --workdir DIR Path to workdir directory for this command.

結論

docker exec の場合 -t のオプションを使用するとcronからは動かない。
docker-compose の場合 -T のオプションを使用しないとcronからは動かない。