As mentioned in app description, app works as a way of informing customers whether they live in serviceable area or not and it wouldn't restrict customers from placing an order. If you really wish to restrict checkouts from customers who don't live in your serviceable zipcodes then its recommended to also use Shopify local delivery feature.
Shopify local delivery works in a checkout flow and we as app developers don't have access to checkout flow so both these apps are perfect companion. This app takes care of validation before checkout and Shopify local delivery takes care of validation during checkout.
We recently launched a feature which would allow you to disable the checkout buttons on a cart page. But note that this feature isn't 100% full proof as there are multiple other ways customers can bypass this validation and directly go to checkout flow.
1. Customer can directly alter page URL to be "/checkout" and bypass "/cart" page.
2. Merchant is using a custom theme with cart being shown as pop-up or sidebar drawer.
3. Customer temporarily disables Javascript to bypass any client side validation.
4. Merchant has "Buy Now" button which allows customers to skip cart page and directly go to checkout page.
This newly launched feature helps a little but we wouldn't recommend using it without properly testing your store setup. If your store has pop-up or cart drawer, functionality wouldn't work. It's best designed if you are using a dedicated "/cart" page for checkout flow.
To play around with this setting you can navigate to "Global Settings" & scroll down to "Disable checkout buttons" feature where you can find various configuration options.
If your cart page has custom checkout buttons which you find are not disabled during your testing then you can choose a custom selectors option at bottom to specify either a name selector or a class selector. If you are unsure about what to input there, please contact our support and we are more than happy to help :)