Zeusmix does not charge a fee for refunds. Refunds for TRC-20, BEP-20, and ERC-20 tokens are made by sending the user the private key that holds their funds.
Anyway, this is the weirdest way, potentially causing further problems since private keys are not supposed to be shared between 2 or more parties. If I somehow get caught on AML radar, I can just withdraw my funds while I file complaint that it wasn't me who did it.
When I know my private key and I shared my private key with you then it's me and you. According to Zeusmix terms, they will share the private key to the customer who is expecting the refund. Which means Zeusmix and the customer only know the private key. The same private key sharing model business was done by a highly established crypto service not long ago. They were doing the business successfully for around half a decade. I do not think this is going to be a problem at all.