The process is very easy
Download the WPuppy plugin. Add this to every website you want to update. Put the key in your own WPuppy environment and set the day and time you want to update.
We update the websites as soon as there is an update. Both core and plugins, scheduled by you.
Before the update we create a backup and screenshots of all pages.
Afterwards we create new screenshots. The software and our people monitor these and you (and your customers) receive an update about the process.