When you are creating variants, is it important to update the "Inventory will be stocked at" field along with the SKU for the item?
For example, if I have items being fulfilled by Printify and ViralStyle, do I need to specify which fulfillment company will be shipping that item?
When I export these listing to Etsy, I don't see somewhere that I can select the fulfillment center.
Is this the correct process when a product is purchased on Etsy.
Etsy Customer purchase -> Etsy sends that info to Shopify -> Shopify locates the SKU and the assigned fulfillment center -> Shopify then sends the shipping info to either Printify or ViralStyle (depending on which company is assigned to the SKU)
In most cases I can think of, yes it's important to have the correct Location assigned to the variant.
This location is what Shopify uses to assign a fulfillment order to the order. This decides which fulfillment service will fulfill your order. In the case of 3rd party fulfillment services, the fulfillment order being assigned to the fulfillment service is often what triggers the fulfillment request, or at least shows where the items should be fulfilled from.