After each purchase from your claim page, ETH is paid out directly to the payout address specified in the claim settings.
Payment for Claims won't display on your Metamask Activity tab as it does not show other people's transactions which transferred crypto to your wallet.
Instead, head over to Etherscan to confirm these Claim transactions.
To verify your Claims being paid out check your internal transactions in Etherscan. You can do this by:
Go to the Etherscan page for your wallet address.
Click on the Internal Txns tab. Here you'll find a list of transactions that may not appear in your Metamask window.