Yes, the authorized user's supplementary card will add up and contribute to the minimum spending requirement of your primary Amex card. So, when you added an AU for your Business Platinum card, it will contribute towards your Biz Plat's minimum spending. If you open a Personal Gold MR card, then you will have to add an AU for the Gold card, and again, spending on THIS supplementary card contributes to the spending of your Personal Gold card.

Amex supplementary cards are NOT free for the Plat and Biz Plat MR cards, in case you're not aware. They do have a fee. But for the Gold and Biz Gold cards, they are free or at least FYF.