There seems to be a necessary field missing from the Adaptive Payments plug-in. In the standard “PayPal” settings in WooCommerce there is a Page Style field. You enter the name of a page style that you create in PayPal and that one is displayed when you checkout.
There is a definitely a problem here, cause seen as there wasn't a field I set the page style I'd created as default in PayPal, and it still wasn't showing up (yet in another WordPress install using standard PayPal of WooC. I see the default style I've set…).