You can also give Hype Data Parser a try… it supports multi-table number files. If you make the CSV export local in your Hype project, you can use it as long as fetch is allowed (meaning in Preview and when deployed to a server, but not on file://).
The workflow involves loading data from the CSV and displaying it in your Hype project using your own solution, Hype Reactive Content, or Hype Data Magic. Now, the client can simply update the tables in Numbers, re-export them, and upload the CSV to the project (via FTP) or use any other online table solution that can be queried via CSV. Update complete.
That said, there are solutions like Airtable, etc., that have a JSON interface, so you don't even need a CSV intermediate step. I mainly created the solution for clients who wanted no dependencies like that (or are offline) and keep sending me their data in Excel spreadsheets.
Here is another approach using SQLite in the browser: