Issue
You want to know what security measures are taken by Heroku Connect as it copies data from your Salesforce Organization to a Heroku Postgres database.
Resolution
Heroku Connect uses TLS encryption while data is in motion both by using HTTPS to your Salesforce org and using TLS while communicating with your Heroku Postgres database. Heroku Connect keeps the unencrypted Salesforce data in memory while transferring the data to/from your Heroku Postgres database.
For information on Heroku Postgres database encryption at rest please see the Heroku Postgres documentation.