It looks like there is a bug in the Xstroe theme that prevents SIMPLE prevents to keep an add-on item that was selected on the product detail page, through to the cart.
It works fine with VARIABLE products.
Workflow:
When selecting a simple item with a single price (like Emily Crib Mattress), I see the add-on product and I can select it but when I go to the cart, it does not carry over.
When I switched themes, it works fine.
