Nokia Lumia 510 - Is the transfer of contacts using Contact Transfer app from another Window Phone 7.x supported?

Yes, direct peer to peer transfer of contacts, although supported, is only recommended when the user doesn’t use or doesn’t want to use a cloud account to sync contacts.

Contacts can also be sync'ed via cloud based sync (via a Microsoft account or other accounts). Whenever possible, this is the recommended way to sync contacts to a Nokia Lumia with Windows Phone in order to avoid duplication of data and be future proof.