Yes, when the miner finds a valid hash, it submits the hash (proof) to the mining contract on Ethereum immediately. The Proof Frequency is merely the expected frequency (the time interval that has the highest likelihood between found proofs) at which valid proofs are found at the particular difficulty associated with that Proof Frequency. What the contract on Ethereum does upon being provided a valid proof is that it mints an amount of KOIN ERC-20 tokens primarily depending on the difficulty of mining at the time when the proof was found and sends it to a wallet address specified by the user of the miner.
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Perfect, thanks for clarifying all that 😃