Hi,
Can you clarify the issue? When you say that their database "filled up", what does this mean, technically? Was there an error message somewhere - and if so, what? UpdraftPlus backups aren't stored inside your WordPress database (they go on the filesystem, and then to cloud storage, depending on what you've got configured), so, more backups than you thought you're taking can't "fill up" the WordPress database. So, I think I need more info to have the full picture.
Best wishes,
David