With customer pricing you can setup auto tag rules that will apply a customer pricing tag when certain conditions are met. This can be done in the "manage tags" section within the app. In the table, you just click on the "create" button under the "auto tagging rules" for the associated tag.
You can setup auto tag rules based on amount of orders made or amount of money spent*. When someone that doesn't have tag reaches these conditions, they will automatically be tagged with that tag. New customers without previous tags will be autotagged but they need to have a customer account.
*Tagging customers by money spent will apply to that account's purchase history in your Shopify store only.