Hmmm … have you tried something like this?
root@DietPi:~# crontab -e
and edit this like:
Edit this file to introduce tasks to be run by cron.
#
# Each task to run has to be defined through a single line
# indicating with different fields when the task will be run
# and what command to run for the task
#
# To define the time you can provide concrete values for
# minute (m), hour (h), day of month (dom), month (mon),
# and day of week (dow) or use '*' in these fields (for 'any').#
# Notice that tasks will be started based on the cron's system
# daemon's notion of time and timezones.
#
# Output of the crontab jobs (including errors) is sent through
# email to the user the crontab file belongs to (unless redirected).
#
# For example, you can run a backup of all your user accounts
# at 5 a.m every week with:
# 0 5 * * 1 tar -zcf /var/backups/home.tgz /home/
#
# For more information see the manual pages of crontab(5) and cron(8)
#
# m h dom mon dow command
00 02 * * * /usr/bin/apt-get update
10 02 * * * /DietPi/dietpi/dietpi-update
20 02 * * * /usr/bin/apt-get upgrade -y
30 02 * * * /usr/bin/apt-get dist-upgrade -y
40 02 * * * /usr/bin/apt-get clean
50 02 * * * /usr/bin/apt-get autoremove -y
00 03 * * * /sbin/reboot