When you import a product to your store in AppScenic, if you want to have its collections automatically imported as well to your online store, then you need to select the box When pushing products to store also push the product to Collection/Categories the first time you import a product.
If you want to have this setup enabled or disabled at a later point, you can go to My Stores and click on ACTIONS on the right side of the store you want to update.
Choose Edit then select (or deselect) the box When pushing products to store also push the product to Collection/Categories. And click on Save.
To check if your collections from AppScenic are synchronized with your online store, just go to My Products and check if the Collections on your AppScenic products corresponds with the ones on your online store.