Hi Yanick,
I’ve checked the package, and it seems that the order confirmation page on your site is using the core URL path. In this case, it loads the default page of your site (which is the homepage). However, the JA Smallbiz homepage uses a special layout that doesn’t include the component block, so the confirmation content doesn’t appear.
I recommend creating menu items from the EasyStore component—for example: EasyStore Cart, EasyStore Checkout, List Orders, etc.—and assigning the default template layout to these menu item pages. That should resolve the issue.

Regards,
Heinz