As a rule database templates are executed on the server unless, as explained in http://www.tersus.com/#Id=3219, the application root model has a clientSideDatabase property set to local and the database action is not in a Service.
It is up to you to decide where data is stored, and of-course that depends on the application needs. For instance, data shared between users should ultimately be stored on the server, while user-specific data can be stored on the client (although client-side databases may be easily lost/erased, so I wouldn't base my application on the assumption that data is safe there, and will probably use client-side data storage for temporary data, and move data needed for the long-term to/from the server.
Note that if client-side database is not used and you have a process which performs multiple database operations (such as multiple Finds), and the entire process is not encapsulated in a service, you are sure to encounter slow performance since each operation incurs a separate client to server call with results sent back to client before the next operation does the same, so make sure you encapsulate such processes in a service. Doing so will also make sure that all database operations share a transaction - see more @ http://www.tersus.com/#Id=320.
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