Thank you for confirming that Automated Tax rates are working as expected now.
So, if the customer lives in a different State, I don’t need to charge him taxes? (I have no idea how taxes work)
That is how the extension works, yes. Basically, if you don’t have a TAX Nexus in the location, then it does not calculate TAX.
That said, we can only help out with configuring the extension itself, and I’d recommend reaching out to a TAX professional who can confirm if it is the right process for your store.
In case you need to collect taxes in multiple locations, you can try other extensions like WooCommerce AvaTax or TaxJar
For any pre-sales questions on those extensions, please open a support request in https://woocommerce.com/contact-us/#sales-form
Is my sites’ tax setup complete?
As far as setting up WooCommerce Services goes, yes. If you’re seeing the TAX rates on the checkout page, it means the setup is complete ??