Unless you are using the Checkout Rates feature (available for US, Canada, and Australia-based accounts using supported stores only), ShipStation does not currently send rates to your selling channel for your customers to select on checkout. For accounts in unsupported countries or using unsupported stores, ShipStation receives the order data only after the checkout is complete.
Many selling channels offer plug-ins you can connect to your carrier accounts that will display live rates to your customers at checkout. If you connect the same carriers to your selling channels as you connect to ShipStation, the live rates provided should be similar.