What to do with runtime generated data spanning several classes?

I'm a self-taught programmer and a lot of the problems I encounter come from a lack of formal education (and often also experience).

My question it the following: How to rationalize where you store the data a class or function creates? I'll make a simple example:

Case: I have a webshop (SHOP) with a REST api and a product provider (PROVIDER) also with a REST API. I determine the product, I send that data to PROVIDER who sends me back formatted data that can be read by SHOP to make a working product on the webshop. PROVIDER also has a secondary REST api that provides generated images.

What I would come up with: I'd make three classes: ProductBase, Shop and Provider
ProductBase would be the class from where I instantiate and store the individual product information.
Shop would be where I design the api interactions with the webshop.
Provider same as shop, but for interactions with provider api.

My problem: At some point you're creating data that's not clearly separated in concern. For example: Would I store the generated product data (from PROVIDER) in the ProductBase instance I created? It feels like I'm coupling the two classes this way. But it not there, then where?
What if I create product images with PROVIDER and I upload them to SHOP? Do I store the uploaded image-url in PRODUCT? How do you keep track of all this info?

The question I want answered:
I've read a lot on OOP and Design Patterns, and I have adopted a TDD approach which has greatly helped to improve my code but I haven't found anything on how to approach the flow of at runtime generated data within software engineering.

What would be a good way to solve above problem(s) and could you explain your rationale for it?