My assumption would be server-level management similar to RDS and Heroku. Since they run on DigitalOcean, I don't think they have much control over the hardware

My assumption would be server-level management similar to RDS and Heroku. Since they run on DigitalOcean, I don't think they have much control over the hardware. Managed at the database/schema/table/etc level does not seem plausible as that would defeat the purpose of a product like this.