Dear Aishwarya,
The efficiency of the TPA is a function of, amongst others, the insurer that you decide. Quite often, 2 issues work simultaneously: (a) The insurers' internal processes for releasing claim funds to the TPA after the processing is done. Few insurers have a electronic transfer of funds directly to the TPA viz United India Insurance. While others, do an audit, manual clearance of funds before they reach the TPA and thence to the employee. (b) The efficiency of the TPA. Some of the better TPA's that I know are regional in nature. When I say this , I mean that while they may be present across the country in terms of offices but really if you see the centralized / decentralized mode of operations, the quality of manpower etc, you will observe wide variations.
Another equally important factor while going in for Mediclaim / health insurance is the quality of Broker / Intermediary that you choose. Their job is not only to get you good quotes from insurance companies but as well to ensure that the claims servicing is smooth. Health insurance policies may have many grey areas where the claim may be processed against the interests of the employee while there can be another way within the policy terms. It is the job of the intermediary ( consultant / Broker) to ensure that the interpretation is presented / done in favour of the employee. More so you should select a partner who has a great value addition in terms of technology that gets extended to your employee.
Broadly - you can check PHS and Medi Assist as prospective partners - they are considered quite strong on servicing group health insurance covers.
Do let me know if you may need any further assistance.
Regards, Deepak