To display Webshipper rates, 3rd party rates needs to be enabled
Check if you have it enabled here:
If you see the truck, it is not enabled and you will need to contact Shopify.
Inform them of the following: "I wish to enable third-party-calculated-shipping rates".
To display your shipping rates directly in your checkout, you need to enable a feature in Shopify called "Third-party calculated shipping rates". This is a subscription limitation set by Shopify.
While the option is included by default in an "Advanced Shopify" subscription, you can contact Shopify support and instantly have it enabled for a smaller plan.
You can do so for an added cost of $20 per month or for free if you are paying for your subscription on an annual basis.
Note: You may have to re-install the Webshipper plugin, if it was already
How to see if it is enabled or not?
Note. if you enable third party rates AFTER you installed the integration in Webshipper, you will need to refresh it again in Webshipper or the integration is not set up.