Indian or Pakistani?

I think we need to distinguish between national Identity & cultural association. From the perspective of national identity you are absolutely right, it is invalid to associate them with Indian identity based on the choice they or their forefathers made at the point of creation of Pakistan, but cultural identity is a different thing.
A pakhtoon living in Mardan is as much an heir to the Pakhtoon culture as a Pakhtoon from Kandahar.
& I believe the same applies to people who migrated from different parts of India....