Shipstation does integrate with WooCommerce natively to pull WooCommerce orders in to Shipstation for fulfillment purposes. When using WooCommerce Warehouses, it is also possible to include the Warehouse ID the WooCommerce order is routed to, within the response from WooCommerce to Shipstation.
This Warehouse ID can be passed to a custom field within Shipstation - both for references purposes, and to support Rules in Shipstation. Automation Rules in Shipstation can then be set to handle an order specifically in Shipstation based on which Warehouse it's been routed to.
First, add your desired Warehouses in your WooCommerce store.
Then, in Shipstation, orders will be pulled in with the corresponding Warehouse ID in either Custom Field 1, 2, or 3. Our support team can assist mapping this as desired.
Then, in ShipStation's Automation Rules, any number of Automation Rules can be added to specifically update an order based on the Warehouse it's routed to.