I see two questions here:
- Should database developers model business logic?
- Should I know how to persist data to the database?
Business logic does not live in a database. It's a conceptual model which must be independent of other layers within your system.
You can always replace one database with another, or you might even decide to use a NoSQL solutions to address potential performance issues.
Database developers can be involved during modelling process, but normally this is done by people with a complete understanding of a problem domain. In our organisation this is done by server side developers.
Many think that database is a foundation of your application. Make poor foundation, and the system will fall. I disagree with this. I see database as a storage medium that can be always replaced.
You should know how to persist data to different storage mediums, including SQL and NoSQL solutions.
Level of required expertise will vary with the size of the system that you are working on.
Small companies would expect you to have that knowledge, when larger companies would normally hire experts to address performance, scalability and security related requirements.
Domain model is a foundation of your system, not the database.
If you work for a small company on a relatively small project, then you should probably design the database yourself.
If you work for a large company on an enterprise system, then it probably makes more sense to pass work to the domain experts.