How do I check the details of all the transferred funds to a particular payee from my ICICI account?

You can check it in Account statement. You can get the account statement by  logging into your net banking a/c. If you have issued cheques in the name of the payee the details of the cheques with their numbers will appear in the pass sheet of your account with the ICICI Bank. If you have transferred funds by NEFT/RTGS/IMPS those details will also be available in the pass sheet.  If cash remittances are made in the account the details of the payee may not be available in the pass sheet but the details can be called for from the bank to prove that those remittances are made to the account of the payee.