That tutorial is actually a bit deprecated since EE now does all of that automatically in this updated tutorial: https://easyengine.io/docs/lets-encrypt/
However if you followed the steps in your originally linked tutorial and edited the crontab file to auto-renew, you'll be fine. You can check this by issuing the command:
crontab -l
to view your crontab (that's lowercase L and not number 1). If that command doesn't show any entries, it means your certificate(s) it will not auto-renew. In that case:
Type crontab -e to open your crontab file in your default editor, and add the followng line:
0 0 1 * * ee site update --le=renew --all 2> /dev/null
Save the crontab file and exit the editor. The above command would check your LE certificates every month on the 1st and renew for all necessary EE sites. Alternatively, you can add:
@monthly ee site update --le=renew --all 2> /dev/null
which is the same command with an easier syntax. You can then type crontab -l to view your crontab to ensure what you just added is actually there.
You can of course also run the command:
ee site update --le=renew --all
to manually check/renew your EE sites right away, or:
ee site update mydomain.com --letsencrypt=renew
for an individual website (replacing mydomain.com with your own website).