By default Shopify stores are set to Manual Fulfilment, you would need to either send each order to Supliful manually by clicking the Request Fulfillment button:
OR you can set your Shopify store to Automatic Fulfillment by visiting the Shopify Settings --> Checkout.
There, scroll down to the Order Processing section, and under the heading After an order has been paid, select Automatically fulfill the order's line items. Don't forget to click the Save button when you are done:
For more information on the Shopify order fulfillment processes please check out this Shopify article here.