Karya Vaikuntham is similar to SriVaikuntham created by Emperuman for a purpose. It is part of the Leela Vibhuti and not part of Nitya Vibhuti. A few Deva-s and devotees who possess a certain type of unique capability have been blessed to go there and worship Emperuman.
Notes:
To understand this – Tiruvenkatamudaiyan graces us with his darshan at Tirumalai. But he also graces us with a similar darshan at several places at temples established by TTD. These are like Tiruvenkatamudaiyan being present at the TTD temples. Emperuman who is at SriVaikuntham is like Tiruvenkatamudaiyan at Tirumalai; Karya Vaikuntha Emperuman is like Tiruvenkatamudaiyan at TTD temples.
Karya Vaikuntham is mirror image of SriVaikuntham – Emperuman will be with the same appearance as that of at SriVaikuntham. But this is not shuddhasatva mayam but is influenced by the three gunas (satva, rajas and tamas). It is part of the material world (prakruti mandalam); mumukshu-s will not desire to go to Karya Vaikuntham as they desire moksham. Moksham will result in reaching SriVaikuntham; hence, they have no business at Karya Vaikuntham.
Those who cannot go to SriVaikuntham will go to Karya Vaikuntham. As part of his leela, if one is ordained to render services at Karya Vaikuntham, they will do so.