Yes, the Schema App WordPress plugin automatically deploys your code. The schema markup is immediately generated for each data item you change, as you edit it. In addition, each data item that refers to the one you're editing (dependent data items) are also regenerated as they would include the changed data. The generation of schema markup is immediate processed for the primary data item, and dependent data is queued for processing over the next few minutes.
As soon as the markup is generated, it is sent onward to the Wordpress site using a Webhook API. The Wordpress Plugin is designed to receive the updated schema markup and immediately update the Wordpress database for the Page URL for the data item (based on the @id).
What happens if we don't see the markup coming through?
I've cleared the cache but still don't see the data, now what?
If after this, you still are unsure, contact the Support team and provide them with an Admin User to diagnose the root cause.