The current design requires the admin to call the function that distributes the tributes, in an ideal world, any one could call that function, but only the admin can decide where the funds go when people do call that function.
In the GIveth Token Distro, we do it like this:
https://github.com/Giveth/giv-token-contracts/blob/9d4c2fb7904c24cd8af7213291d91747722495bb/contracts/TokenDistro/TokenDistro.sol#L171
Very simple, if people are owed funds, anyone can push the funds to the destination address. This makes it easy for multisigs and other contracts to receive the funds that accumulate, and we also have found other benefits, for instance, our accountant can claim funds for us and then get an accurate balances when we do our monthly audits.