Hi Suja, An interesting question. Really the answer lies with the application tier. There is no native way within Delphix to direct traffic. The answer would be exactly the same as if you had physical databases. A VDB is just a database at the end of a connection string, your application would have to determine which connection it made.
If you wanted to run these tests automatically against different datasets based on a schedule rather than in real-time then I'd suggest taking a look at the Self-service Branching capability (or bookmarking).
Branching allows you to store different versions of data in a minimal storage footprint and alter the version using the self-service interface (activate a branch) or using the public REST API. In this way you can maintain a single connection string but alter the database data by activating different branches. Since this can be done using our self-service API - or even better through Marcin Przepiorowski's wonderful dxToolkit a wrapper around the REST API's implemented in Perl or as an executable) - you can implement an automated test strategy without ever having to talk to a DBA (I exaggerate here of course, for effect). In this way by establishing based on the test criteria what test data you need you can activate programmatically the correct set of data by activating the appropriate Branch.
The Self-service concepts are detailed here. The dxToolkit is here.