Updating our extensions should not make any problems to you. However it may be conflicting with other extensions that are not up to date or from time to time can conflict with solutions that were implemented (this is why it's recommended to make a backup even when you're updating Joomla core!). This is why it's worth and secure to proceed with the updates the way we explain below.
Another copy of your website
It's good to have the copy of current Joomla installation somewhere on your server so you can test the changes you're making and updates you're performing.
Some hosting providers lets you to have staging installation so you can mirror your production and test installation.
If it's not the case, you can easily do it yourself by installing the copy of your production installation in other place (it can be same or another server like localhost). You can easily make and restore your production site using Akeeba Backup.
Then proceed with the updates and check if all works fine. If it does just apply all the changes on your production site.
If you don't want to have another copy of your website
If you don't decide to have the testing environment and want to do all on production site these are our suggestions to make it more secure if something breaks.
- Make a backup of your site before doing any update (use Akeeba Backup) and save it securely locally
- Make sure your Joomla! installtion is up to date - see how to update Joomla
- Update the extension - you can do it either by using Update Manager or manually by installing most recent version over the existing one
- Check if all works fine - if something is wrong you can always revert to previous version of your website by bringing back the backup you did in point 1.