Currently, ShippingEasy does not send you or your customer a Shipment Confirmation e-mail for drop shipped ("Mark as Shipped") orders. Only orders with labels generated in ShippingEasy will receive the Shipment Confirmation email. However, using "Marked as Shipped" does update your SHIPMENT HISTORY page and your website with the tracking number.
I did notice in your Shopify Store Settings within ShippingEasy that it is currently selected to 'Request that Shopify send shipment notification to buyer' so we are not sending any confirmation emails for this store. It is likely that the confirmation emails are coming from Shopify.
I hope that helps, but if you have any further questions, feel free to reach out to our support team.