When you import a product from 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. (See below)
If you want to have this setup enabled or disabled at a later point, you can go to Integrations 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. Then click on SAVE.
To be sure that your collections from AppScenic are synchronized with your online store, just go to My Products, then click on Collections. Here, you check if your AppScenic collections correspond with the ones on your online store.