Why does free shipping apply on my live store when the cart drawer is only on a draft theme? (Essential Cart Drawer app)
A spend tier with the reward type Shipping discount is a Shopify automatic discount. Once your cart drawer is published, Shopify applies it to every checkout in your store, whatever theme the customer shopped on.
The admin shows this under the reward type: Applies to all checkouts in your store.
To test without touching live customers, use a separate test store, or set the tier to Visual spend tier only while you test. Change it back to Shipping discount when you go live.
See also How to Set Up Spend Tiers on Cart Drawer.